New tracks for future computational platforms for engineering applications

The purpose of this paper is to address new tracks for the future generation ofcomputational applications in mechanics and related branches. We advocate thatmodern computational tools will have to deal with complex strongly coupled multi-physics multi-scale problems. Moreover, heterogeneous distributed multi-processorssystems are used today for the numerical simulations. We pose here some basicideas for the design of modern computational applications. All the illustrations arebased on finite elements strategies implemented in a pure Java paradigm

Local Projection-Based Stabilized Mixed Finite Element Methods for Kirchhoff Plate Bending Problems

Based on stress-deflection variational formulation, we propose a family of local projection-based stabilized mixed finite element methods for Kirchhoff plate bending problems. According to the error equations, we obtain the error estimates of the approximation to stress tensor in energy norm. And by duality argument, error estimates of the approximation to deflection in H1-norm are achieved. Then we design an a posteriori error estimator which is closely related to the equilibrium equation, constitutive equation, and nonconformity of the finite element spaces. With the help of Zienkiewicz-Guzmán-Neilan element spaces, we prove the reliability of the a posteriori error estimator. And the efficiency of the a posteriori error estimator is proved by standard bubble function argument

Finite element pressure stabilizations for incompressible flow problems

Discretizations of incompressible flow problems with pairs of finite element spaces that do not satisfy a discrete inf-sup condition require a so-called pressure stabilization. This paper gives an overview and systematic assessment of stabilized methods, including the respective error analysis

Computational Engineering

This Workshop treated a variety of finite element methods and applications in computational engineering and expanded their mathematical foundation in engineering analysis. Among the 53 participants were mathematicians and engineers with focus on mixed and nonstandard finite element schemes and their applications

Modeling the hydro-mechanical responses of strip and circular punch loadings on water-saturated collapsible geomaterials

A stabilized enhanced strain finite element procedure for poromechanics is fully integrated with an elasto-plastic cap model to simulate the hydro-mechanical interactions of fluid-infiltrating porous rocks with associative and non-associative plastic flow. We present a quantitative analysis on how macroscopic plastic volumetric response caused by pore collapse and grain rearrangement affects the seepage of pore fluid, and vice versa. Results of finite element simulations imply that the dissipation of excess pore pressure may significantly affect the stress path and thus alter the volumetric plastic responses

Coupled space-time discontinuous Galerkin method for dynamical modeling in porous media

This thesis deals with coupled space-time discontinuous Galerkin methods for the modeling of dynamical phenomena in fluid saturated porous media. The numerical scheme consists of finite element discretizations in the spatial and in the temporal domain simultaneously. In particular, two major classes of approaches have been investigated. The first one is the so-called time-discontinuous Galerkin (DGT) method, consisting of discontinuous polynomials in the temporal domain but continuous ones in space. A natural upwind flux treatment is introduced to enforce the continuity condition at discrete time levels. The proposed numerical approach is suitable for solving first-order time-dependend equations. For the second-order equations, an Embedded Velocity Integration (EVI) technique is developed to degenerate a second-order equation into a first-order one. The resulting first-order differential equation with the primary variable in rate term (velocity) can in turn be solved by the time-discontinuous Galerkin method efficiently. Applications concerning both the first- and second-order differential equations as well as wave propagation problems in porous materials are investigated. The other one is the coupled space-time discontinuous Galerkin (DGST) method, in which neither the spatial nor the temporal approximations pocesses strong continuity. Spatial fluxes combined with flux-weighted constraints are employed to enforce the interelement consistency in space, while the consistency in the time domain is enforced by the temporal upwind flux investigated in the DGT method. As there exists no coupling between the spatial and temporal fluxes, various flux treatments in space and in time are employed independently. The resulting numerical scheme is able to capture the steep gradients or even discontinuities. Applications concerning the single-phase flow within the porous media are presented.Im Rahmen dieser Arbeit werden gekoppelte Raum-Zeit Finite-Element-Methoden für die Simulation dynamischer Effekte in fluid-gesättigten porösen Materialien entwickelt und numerisch umgesetzt. Dazu wird eine gekoppelte Diskretisierung des räumlichen und zeitlichen Gebietes vorgenommen. Insbesondere werden zwei Klassen von Verfahren untersucht. Die erste Methode ist ein sogenanntes zeitlich-diskontinuierliches Galerkin Verfahren (DGT-Methode). Hierbei werden diskontinuierliche Ansätze in der Zeit und kontinuierliche Ansätze im Raum verwendet. Die Kontinuitätsnebenbedingung in der Zeit wird durch einen upwind-Flussterm erzwungen. Der Flussterm unterliegt mathematischen Restriktionen und daher ist das resultierende Finite Element Verfahren nur für Gleichungen mit zeitlichen Ableitungen erster Ordnung geeignet. Um auch Gleichungen zweiter Ordnungen mit dem entwickelten DGT-Verfahren behandeln zu können, ist die EVI-Methode (Embedded Velocity Integration method) entwickelt worden. Im Rahmen der EVI-Technik wird die Geschwindigkeit als Primärvariable gewählt und im Bezug auf die gewählten zeitlichen Ansätze integriert. Die auf der Geschwindigkeit basierenden schwachen Formen können wiederum mit der DGT-Methode gelöst werden. Die entwickelten numerischen Raum-Zeit Finite-Elemente-Methoden werden sowohl für elastische Wellenausbreitungsprobleme als auch für gekoppelte Fragestellungen in porösen Medien angewendet. Abschließend wird ein räumlich diskontinuierliches Finite-Element-Verfahren entwickelt und mit den bereits entwickelten zeitlich-diskontinuierlichen Methoden gekoppelt. Die räumliche Kontinuitätsbedingung wird durch die Entwicklung eines speziellen Flusstermes erzwungen. Es wird gezeigt, dass sich das Verfahren mit den bereits entwickelten Flusstermen für die zeitliche Kontinuität koppeln lässt. Dies wird durch die Entkopplung der räumlichen und zeitlichen Flussterme möglich. Das resultierende Raum-Zeit diskontinuierliche Finite-Element-Verfahren wird wiederum auf Strömungsprobleme mischbarer Fluide in porösen Medien angewendet und mit klassischen Methoden verglichen