Almae Matris Studiorum Campus

Ricci, Alessandro

SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency 1
Sistemi Concorrenti e di Rete LS
II Facoltà di Ingegneria - Cesena
a.a 2008/2009
[module lab 2.2] 
GUI FRAMEWORKS & 
CONCURRENCY
v1.0 BETA
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency
GUI FRAMEWORKS & CONCURRENCY
• Once upon a time GUI applications were single-threaded...
– GUI events processed by a “main event loop”
• ..modern GUI Frameworks are not so different
– creating a dedicated event dispatch thread (EDT) for handling GUI 
events
– the thread fetches events off a queue and dispatches them to 
application-defined event handlers
• Most of the modern GUI Frameworks are single-threaded
– Java, QT, NextStep, Mac OS Cocoa, XWindow...
• Multithreaded GUI as a “failed dream” [*]
– many attempts, failed due to the generation of problems with race 
conditions and deadlock
2
[*] referred in this way  by Sun VP Graham Hamilton in his blog 
http://weblogs.java.net/blog/kgh/archive/2004/10
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency
MULTITHREADED GUI FRAMEWORKS: 
THE PROBLEM
• Clash between input event processing and OO modelling of GUI 
components
– that can easily lead to deadlocks and race conditions
• Inconsistent lock ordering 
– in managing user-initiated actions and application-initiated actions 
• user actions “bubble up” from OS to the application
– OS mouse click ->mouse click event of the GUI toolkit -> high-level event of the 
application listener...
• application-actions “bubble down” from application to action
– changing background color of a component at the application level ->  disptached 
to component class -> dispatched to OS for rendering,,,
• most of the actions need to lock objects
– model-view-control (MVC) pattern 
• the control calls into the model, which notifies the view that something has 
changed...
• ...but the controller calls also the view, which may in turn call back into the 
model to query the model state
3
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency
SINGLE-THREADED GUI
• Achieving thread-safety via thread-confinement
– all GUI objects are accessed exclusively by the event thread
• including visual components and data models 
– the application developer must make sure that these objects are properly 
confined
• Sequential event processing
– events like kind of task to be processed sequentially by the event thread
• Problems and challenges
– if one task takes long time to execute, other task must wait
• blocking the overall GUI
> ...so tasks that execute in the event-thread must return quickly
– to initiate a long-term task a separate thread must be used
• es: spell-checking a document, searching the file system
> ...but typically a long-term task must provide a visual feedback for 
indicating progress or when it completes
• and this code need to be executed by the event thread...
4
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency
THREAD CONFINEMENT IN SWING
• All Swing components (such as JButton and JTable) and data 
models (e.g. Table Model and Tree Model) are confined to the event 
thread 
– any code that access these objects must run in the event thread
• Exceptions
– Swing methods that can be safely called from any thread
• clearly identified in the Javadoc as thread-safe
5
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency
THREAD-SAFE SWING METHODS
• Thread-Safe methods
– SwingUtilities.isEventDispatchThread
• to check if the current thread is the event thread
– SwingUtilities.invokeLater
• to schedule a Runnable for execution on the event thread 
– SwingUtilities.invokeAndWait
• to schedule a Runnable task for execution on the event thread, blocking the 
current thread until it completes
• cannot be called by the event thread
– methods to enqueue and repaint or revalidation request on the event 
queue
– methods for adding or removing listeners
• can be called from any thread, but listeners will always be invoked in the 
event thread
• The swing event thread can be thought as a single-thread Executor 
that processes tasks from the event queue
– invokeLater and invokeAndWait used to submit new tasks to 
execute
6
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency
A SIMPLE GUI EXECUTOR
• Executor delegating tasks to SwingUtilities for executions
7
public class GuiExecutor extends AbstractExecutorService {
    // Singletons have a private constructor and a public factory
    private static final GuiExecutor instance = new GuiExecutor();
    private GuiExecutor() { }
    public static GuiExecutor instance() { return instance; }
    public void execute(Runnable r) {
        if (SwingUtilities.isEventDispatchThread())
            r.run();
        else
            SwingUtilities.invokeLater(r);
    }
    // Plus trivial implementations of lifecycle methods
}
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency
SHORT-RUNNING GUI TASKS
• Can be executed directly by the event thread
• Simple example
• The control never leaves the event thread
– the event originates in the GUI toolkit, is delivered to the application, the 
application modifies the GUI in response to user’s action
8
final Random random = new Random();
final JButton button = new JButton("Change Color");
...
button.addActionListener(new ActionListener() {
    public void actionPerformed(ActionEvent e) {
        button.setBackground(new Color(random.nextInt()));
    }
});
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency
LONG-RUNNING TASKS
• Some of the processing must be offloaded to another thread
– exploiting executors
• Two main cases
– long-term task without visual feedbacks
• simple case, quite unfrequent
– long-term task with visual feedbacks
• complex case, most frequent
9
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency
BINDING A TASK 
WITHOUT VISUAL FEEDBACKS
• Exploiting a simple separated executor (or thread)
• Example:
10
ExecutorService backgroundExec = Executors.newCachedThreadPool();
...
button.addActionListener(new ActionListener() {
    public void actionPerformed(ActionEvent e) {
        backgroundExec.execute(new Runnable() {
            public void run() { doBigComputation(); }
        });
}});
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency
LONG-RUNNING TASK WITH USER FEEDBACKS
• The long-running task must submit another task to run in the event 
thread whenever the user interface must be updated
• Example:
11
button.addActionListener(new ActionListener() {
    public void actionPerformed(ActionEvent e) {
        button.setEnabled(false);
        label.setText("busy");
        backgroundExec.execute(new Runnable() {
            public void run() {
                try {
                    doBigComputation();
                } finally {
                    GuiExecutor.instance().execute(new Runnable() {
                        public void run() {
                            button.setEnabled(true);
                            label.setText("idle");
                        }
                    });
                }
            }
        });
    }
});
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency
SwingWorker
• Java 6.0 provides auxiliary classes for making it easier to program 
complex long-term tasks that can interact with the GUI
• SwingWorker class
– provide a direct support for task cancellation, completion notification and 
progress indication
12
class SwingWorker<T,V> implements RunnableFuture<T> {
  ...
  // to be overridden
  protected abstract  T doInBackground(); 
  protected  void  done()
  protected final void publish(V... chunks)
  protected void process(List<V> chunks);  
  ...
  // to be directly used
  boolean cancel(boolean mayInterruptIfRunning);
  protected  void setProgress(int progress);  
  ...  
}
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency
TASK EXECUTION AND INTERFACE 
UPDATE
• Support for asynchronous task execution & consequent interface 
update
– doInBackground
• encapsulate the computational body of the task to be executed 
asynchronously w.r.t. GUI activity, computing a result or throwing an 
exception if unable to do so
• executed by some thread, not by the Swing EDT
– done
• encapsulate the action to do on the GUI when the task completed
• executed by the Swing EDT
• Support for asynchonous update of interfaces
– publish(V... chunks)
• used from inside doInBackground to deliver intermediate results for 
processing on the Event Dispatch Thread inside the process method
– process(List<V> chunks);  
• receives data chunks from the publish method asynchronously on the EDT
13
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency
AN EXAMPLE: SWING WORKER TEST
14
class CounterTask extends SwingWorker<Integer, Integer> { 
  protected Integer doInBackground() throws Exception { 
    int i = 0;
    int sum = 0; 
    int maxCount = 10; 
    while (!isCancelled() && i < maxCount) { 
      sum+=i;
      i++; 
      publish(new Integer[] { i }); 
      setProgress(100 * i / maxCount); 
      Thread.sleep(1000); 
    } 
    return sum; 
  } 
    
  protected void process(List<Integer> chunks) { 
    for (int i : chunks) 
      System.out.println("Step "+i); 
  } 
  protected void done() { 
    if (isCancelled()){ 
      System.out.println("Task cancelled."); 
    } else { 
      System.out.println("Task completed."); 
    }
  } 
} 
SISCO LS - II Facoltà Ingegneria - Cesena GUI Frameworks & Concurrency 15
public class SwingWorkerTest {
  public static void main(String[] args) {
    JTextArea textArea = new JTextArea(10, 20);
    JProgressBar progressBar = new JProgressBar(0, 100);
    CounterTask task = new CounterTask();
    JButton startButton = new JButton("Start");
    startButton.addActionListener(new ActionListener() {
       public void actionPerformed(ActionEvent e) { task.execute();}});
    JButton cancelButton = new JButton("Cancel");
    cancelButton.addActionListener(new ActionListener() {
       public void actionPerformed(ActionEvent e) { task.cancel(true); }});
    task.addPropertyChangeListener(new PropertyChangeListener() {
       public void propertyChange(PropertyChangeEvent evt) {
 if ("progress".equals(evt.getPropertyName())) {
   progressBar.setValue((Integer) evt.getNewValue());
 }
       }
    });
    
    JPanel buttonPanel = new JPanel();
    buttonPanel.add(startButton);
    buttonPanel.add(cancelButton);
    JPanel cp = new JPanel();
    LayoutManager layout = new BoxLayout(cp, BoxLayout.Y_AXIS);
    cp.setLayout(layout);
    cp.add(buttonPanel);
    cp.add(new JScrollPane(textArea));
    cp.add(progressBar);
    JFrame frame = new JFrame("SwingWorker Test");
    frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    frame.setContentPane(cp);
    frame.pack();
    frame.setVisible(true);
  }
}


English

module-lab-2.2-GUI Frameworks and Concurrency

Figini, Paolo

Materiale per lezione su sviluppo e istituzioni (1)

Giovannucci, Chiara

 United Nations A/RES/57/18 
 
General Assembly Distr.: General 24 January 2003 
Fifty-seventh session 
Agenda item 155 
 
02 53898 
Resolution adopted by the General Assembly 
[on the report of the Sixth Committee (A/57/562 and Corr.1)] 
  57/18. Model Law on International Commercial Conciliation of 
the United Nations Commission on International Trade 
Law 
 
 
 The General Assembly, 
 Recognizing the value for international trade of methods for settling 
commercial disputes in which the parties in dispute request a third person or persons 
to assist them in their attempt to settle the dispute amicably, 
 Noting that such dispute settlement methods, referred to by expressions such 
as conciliation and mediation and expressions of similar import, are increasingly 
used in international and domestic commercial practice as an alternative to 
litigation, 
 Considering that the use of such dispute settlement methods results in significant 
benefits, such as reducing the instances where a dispute leads to the termination of a 
commercial relationship, facilitating the administration of international transactions by 
commercial parties and producing savings in the administration of justice by States, 
 Convinced that the establishment of model legislation on these methods that is 
acceptable to States with different legal, social and economic systems would 
contribute to the development of harmonious international economic relations, 
 Noting with satisfaction the completion and adoption by the United Nations 
Commission on International Trade Law of the Model Law on International 
Commercial Conciliation,1 
 Believing that the Model Law will significantly assist States in enhancing their 
legislation governing the use of modern conciliation or mediation techniques and in 
formulating such legislation where none currently exists, 
 Noting that the preparation of the Model Law was the subject of due 
deliberation and extensive consultations with Governments and interested circles, 
_______________ 
1 Official Records of the General Assembly, Fifty-seventh Session, Supplement No. 17 (A/57/17), annex I. 
 
A/RES/57/18 
2 
 Convinced that the Model Law, together with the Conciliation Rules 
recommended by the General Assembly in its resolution 35/52 of 4 December 1980, 
contributes significantly to the establishment of a harmonized legal framework for the 
fair and efficient settlement of disputes arising in international commercial relations, 
 1. Expresses its appreciation to the United Nations Commission on 
International Trade Law for completing and adopting the Model Law on 
International Commercial Conciliation, the text of which is contained in the annex 
to the present resolution, and for preparing the Guide to Enactment and Use of the 
Model Law; 
 2. Requests the Secretary-General to make all efforts to ensure that the 
Model Law, together with its Guide to Enactment, becomes generally known and 
available; 
 3. Recommends that all States give due consideration to the enactment of 
the Model Law, in view of the desirability of uniformity of the law of dispute 
settlement procedures and the specific needs of international commercial 
conciliation practice. 
52nd plenary meeting 
19 November 2002 
 
 
  Annex 
 
  Model Law on International Commercial Conciliation of the United Nations 
Commission on International Trade Law 
 
 
  Article 1 
Scope of application and definitions 
 
1. This Law applies to international2 commercial3 conciliation. 
2. For the purposes of this Law, “conciliator” means a sole conciliator or two or 
more conciliators, as the case may be. 
3. For the purposes of this Law, “conciliation” means a process, whether referred 
to by the expression conciliation, mediation or an expression of similar import, 
whereby parties request a third person or persons (“the conciliator”) to assist them 
in their attempt to reach an amicable settlement of their dispute arising out of or 
relating to a contractual or other legal relationship. The conciliator does not have the 
authority to impose upon the parties a solution to the dispute. 
4. A conciliation is international if: 
_______________ 
2 States wishing to enact this Model Law to apply to domestic as well as international conciliation may 
wish to consider the following changes to the text: 
– Delete the word “international” in paragraph 1 of article 1; and  
– Delete paragraphs 4, 5 and 6 of article 1. 
3 The term “commercial” should be given a wide interpretation so as to cover matters arising from all 
relationships of a commercial nature, whether contractual or not. Relationships of a commercial nature 
include, but are not limited to, the following transactions: any trade transaction for the supply or exchange 
of goods or services; distribution agreement; commercial representation or agency; factoring; leasing; 
construction of works; consulting; engineering; licensing; investment; financing; banking; insurance; 
exploitation agreement or concession; joint venture and other forms of industrial or business cooperation; 
carriage of goods or passengers by air, sea, rail or road. 
 
A/RES/57/18 
3 
 (a) The parties to an agreement to conciliate have, at the time of the 
conclusion of that agreement, their places of business in different States; or 
 (b) The State in which the parties have their places of business is different 
from either: 
 (i) The State in which a substantial part of the obligations of the commercial 
relationship is to be performed; or 
 (ii) The State with which the subject matter of the dispute is most closely 
connected. 
5. For the purposes of this article: 
 (a) If a party has more than one place of business, the place of business is 
that which has the closest relationship to the agreement to conciliate; 
 (b) If a party does not have a place of business, reference is to be made to 
the habitual residence of the party. 
6. This Law also applies to a commercial conciliation when the parties agree that 
the conciliation is international or agree to the applicability of this Law. 
7. The parties are free to agree to exclude the applicability of this Law. 
8. Subject to the provisions of paragraph 9of this article, this Law applies 
irrespective of the basis upon which the conciliation is carried out, including 
agreement between the parties whether reached before or after a dispute has arisen, 
an obligation established by law, or a direction or suggestion of a court, arbitral 
tribunal or competent governmental entity. 
9. This Law does not apply to: 
 (a) Cases where a judge or an arbitrator, in the course of judicial or arbitral 
proceedings, attempts to facilitate a settlement; and 
 (b) [...]. 
 
  Article 2 
Interpretation 
 
1. In the interpretation of this Law, regard is to be had to its international origin 
and to the need to promote uniformity in its application and the observance of good 
faith. 
2. Questions concerning matters governed by this Law which are not expressly 
settled in it are to be settled in conformity with the general principles on which this 
Law is based. 
 
  Article 3 
Variation by agreement 
 
 Except for the provisions of article 2 and article 6, paragraph3, the parties may 
agree to exclude or vary any of the provisions of this Law. 
 
A/RES/57/18 
4 
  Article 4 
Commencement of conciliation proceedings4 
 
1. Conciliation proceedings in respect of a dispute that has arisen commence on 
the day on which the parties to that dispute agree to engage in conciliation 
proceedings. 
2. If a party that invited another party to conciliate does not receive an 
acceptance of the invitation within thirty days from the day on which the invitation 
was sent, or within such other period of time as specified in the invitation, the party 
may elect to treat this as a rejection of the invitation to conciliate. 
 
  Article 5 
Number and appointment of conciliators 
 
1. There shall be one conciliator, unless the parties agree that there shall be two 
or more conciliators. 
2. The parties shall endeavour to reach agreement on a conciliator or conciliators, 
unless a different procedure for their appointment has been agreed upon. 
3. Parties may seek the assistance of an institution or person in connection with 
the appointment of conciliators. In particular: 
 (a) A party may request such an institution or person to recommend suitable 
persons to act as conciliator; or 
 (b) The parties may agree that the appointment of one or more conciliators 
be made directly by such an institution or person. 
4. In recommending or appointing individuals to act as conciliator, the institution 
or person shall have regard to such considerations as are likely to secure the 
appointment of an independent and impartial conciliator and, where appropriate, 
shall take into account the advisability of appointing a conciliator of a nationality 
other than the nationalities of the parties. 
5. When a person is approached in connection with his or her possible 
appointment as conciliator, he or she shall disclose any circumstances likely to give 
rise to justifiable doubts as to his or her impartiality or independence. A conciliator, 
from the time of his or her appointment and throughout the conciliation 
proceedings, shall without delay disclose any such circumstances to the parties 
unless they have already been informed of them by him or her. 
 
_______________ 
4 The following text is suggested for States that might wish to adopt a provision on the suspension of the 
limitation period: 
Article […] Suspension of limitation period 
 1. When the conciliation proceedings commence, the running of the limitation period regarding the claim 
that is the subject matter of the conciliation is suspended.  
2. Where the conciliation proceedings have terminated without a settlement agreement, the limitation 
period resumes running from the time the conciliation ended without a settlement agreement. 
A/RES/57/18 
5 
  Article 6 
Conduct of conciliation 
 
1. The parties are free to agree, by reference to a set of rules or otherwise, on the 
manner in which the conciliation is to be conducted. 
2. Failing agreement on the manner in which the conciliation is to be conducted, 
the conciliator may conduct the conciliation proceedings in such a manner as the 
conciliator considers appropriate, taking into account the circumstances of the case, 
any wishes that the parties may express and the need for a speedy settlement of the 
dispute. 
3. In any case, in conducting the proceedings, the conciliator shall seek to 
maintain fair treatment of the parties and, in so doing, shall take into account the 
circumstances of the case. 
4. The conciliator may, at any stage of the conciliation proceedings, make 
proposals for a settlement of the dispute. 
 
  Article 7 
Communication between conciliator and parties 
 
 The conciliator may meet or communicate with the parties together or with 
each of them separately. 
 
  Article 8 
Disclosure of information 
 
 When the conciliator receives information concerning the dispute from a party, 
the conciliator may disclose the substance of that information to any other party to 
the conciliation. However, when a party gives any information to the conciliator, 
subject to a specific condition that it be kept confidential, that information shall not 
be disclosed to any other party to the conciliation. 
 
  Article 9 
Confidentiality 
 
 Unless otherwise agreed by the parties, all information relating to the 
conciliation proceedings shall be kept confidential, except where disclosure is 
required under the law or for the purposes of implementation or enforcement of a 
settlement agreement. 
 
  Article 10 
Admissibility of evidence in other proceedings 
 
1. A party to the conciliation proceedings, the conciliator and any third person, 
including those involved in the administration of the conciliation proceedings, shall 
not in arbitral, judicial or similar proceedings rely on, introduce as evidence or give 
testimony or evidence regarding any of the following: 
 (a) An invitation by a party to engage in conciliation proceedings or the fact 
that a party was willing to participate in conciliation proceedings; 
 (b) Views expressed or suggestions made by a party in the conciliation in 
respect of a possible settlement of the dispute; 
 (c) Statements or admissions made by a party in the course of the 
conciliation proceedings; 
A/RES/57/18 
6 
 (d) Proposals made by the conciliator; 
 (e) The fact that a party had indicated its willingness to accept a proposal for 
settlement made by the conciliator; 
 (f) A document prepared solely for purposes of the conciliation proceedings. 
2. Paragraph 1 of this article applies irrespective of the form of the information 
or evidence referred to therein. 
3. The disclosure of the information referred to in paragraph 1 of this article shall 
not be ordered by an arbitral tribunal, court or other competent governmental 
authority and, if such information is offered as evidence in contravention of 
paragraph 1 of this article, that evidence shall be treated as inadmissible. 
Nevertheless, such information may be disclosed or admitted in evidence to the 
extent required under the law or for the purposes of implementation or enforcement 
of a settlement agreement. 
4. The provisions of paragraphs 1, 2 and 3 of this article apply whether or not the 
arbitral, judicial or similar proceedings relate to the dispute that is or was the 
subject matter of the conciliation proceedings. 
5. Subject to the limitations of paragraph 1 of this article, evidence that is 
otherwise admissible in arbitral or judicial or similar proceedings does not become 
inadmissible as a consequence of having been used in a conciliation. 
 
  Article 11 
Termination of conciliation proceedings 
 
 The conciliation proceedings are terminated: 
 (a) By the conclusion of a settlement agreement by the parties, on the date of 
the agreement; 
 (b) By a declaration of the conciliator, after consultation with the parties, to 
the effect that further efforts at conciliation are no longer justified, on the date of the 
declaration; 
 (c) By a declaration of the parties addressed to the conciliator to the effect 
that the conciliation proceedings are terminated, on the date of the declaration; or 
 (d) By a declaration of a party to the other party or parties and the 
conciliator, if appointed, to the effect that the conciliation proceedings are 
terminated, on the date of the declaration. 
 
  Article 12 
Conciliator acting as arbitrator 
 
 Unless otherwise agreed by the parties, the conciliator shall not act as an 
arbitrator in respect of a dispute that was or is the subject of the conciliation 
proceedings or in respect of another dispute that has arisen from the same contract 
or legal relationship or any related contract or legal relationship. 
 
  Article 13 
Resort to arbitral or judicial proceedings 
 
 Where the parties have agreed to conciliate and have expressly undertaken not 
to initiate during a specified period of time or until a specified event has occurred 
arbitral or judicial proceedings with respect to an existing or future dispute, such an 
A/RES/57/18 
7 
undertaking shall be given effect by the arbitral tribunal or the court until the terms 
of the undertaking have been complied with, except to the extent necessary for a 
party, in its opinion, to preserve its rights. Initiation of such proceedings is not of 
itself to be regarded as a waiver of the agreement to conciliate or as a termination of 
the conciliation proceedings. 
 
  Article 14 
Enforceability of settlement agreement5 
 
 If the parties conclude an agreement settling a dispute, that settlement 
agreement is binding and enforceable ... [the enacting State may insert a description 
of the method of enforcing settlement agreements or refer to provisions governing 
such enforcement]. 
 
_______________ 
5 When implementing the procedure for enforcement of settlement agreements, an enacting State may 
consider the possibility of such a procedure being mandatory. 


ML on international commercial conciliation 2002

Baroncini, Elisa

WTO Agreement (with the scheme of WTO multilateral and plurilateral agreements)

Goffredo, Stefano

Unite research with what citizens do for fun:

‘‘recreational monitoring’’ of marine biodiversity

Contributo di carattere introduttivo: criteri esterni ed esterni per l'attribuzione ad Origene di Cod. Gr. 314 (Bayerische Staatsbibliothek, München)

Perrone, Lorenzo

Rediscovering Origen Today: First Impressions of the New Collection of Homilies on the Psalms in the Codex Monacensis Graecus 314

Guerra, Maria Letizia

CONFIDENCE INTERVALS FOR TOURISM DEMAND ELASTICITY

Chiesa, Gabriella

Optimal Credit Risk Transfer, Monitored Finance, and Banks

Lanza, Alessandro

 UNIVERSITY OF BOLOGNA – FACULTY OF ENGINEERING 
INTERNATIONAL MASTER COURSE IN CIVIL ENGINEERING 2010/2011 
***  Finite Element Analysis  *** 
 
 
Pag. 1 di 1 
 
LAB3:   2D ELLIPTIC PROBLEMS 
Download from  http://campus.cib.unibo.it/cgi/lista  (ricerca per docente -> Lanza) the FEA_LAB3.zip 
file, then unzip it. 
 
In FreeFem++, find approximate solutions of the following 2-D elliptic BVP (Boundary Value Problem) 
by means of the GFEM (Galerkin Finite Element Method) with linear and quadratic elements: 
 
1)  Mixed (Dirichlet-Neumann) BVP: 
 





Γ∈=⋅∇
Γ∈=
=Ω∈=∆−
ConditionBoundaryNeumannousInhomogeneyxnu
ConditionBoundaryDirichletsHomogeneouyxyxu
equationsPoissoncircleunityxyxfyxu
N
D
),(2ˆ
),(0),(
'),(),(),(
 
 
 where  ( ))1sin()()1cos(4),( 222222 −++−−+−= yxyxyxyxf  
            and      { }])3/4(,0[),sin(),cos(:),( 2 π∈==∈=Γ ttytxRyxD  
 
Compare the approximate solutions obtained by changing the domain triangulation (compute the L
2
 and 
H
1
 errors) with the exact solution: 
)1sin(),(
22 −+= yxyxu  
 


FEA_LAB3

Taylor, Peter Grenville

Subjunctive Clauses & Inflection in English

University of Bologna

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