A conservative fully-discrete numerical method for the regularised shallow water wave equations

The paper proposes a new, conservative fully-discrete scheme for the numerical solution of the regularised shallow water Boussinesq system of equations in the cases of periodic and reflective boundary conditions. The particular system is one of a class of equations derived recently and can be used in practical simulations to describe the propagation of weakly nonlinear and weakly dispersive long water waves, such as tsunamis. Studies of small-amplitude long waves usually require long-time simulations in order to investigate scenarios such as the overtaking collision of two solitary waves or the propagation of transoceanic tsunamis. For long-time simulations of non-dissipative waves such as solitary waves, the preservation of the total energy by the numerical method can be crucial in the quality of the approximation. The new conservative fully-discrete method consists of a Galerkin finite element method for spatial semidiscretisation and an explicit relaxation Runge--Kutta scheme for integration in time. The Galerkin method is expressed and implemented in the framework of mixed finite element methods. The paper provides an extended experimental study of the accuracy and convergence properties of the new numerical method. The experiments reveal a new convergence pattern compared to the standard, non-conservative Galerkin methods

Zur Qualitaet der Bundesrepublik als Standort fuer Investitionen und Kapitalanlage. Wachstumsfoerdernde Orientierung unserer Wirtschafts- und Finanzpolitik / Wolfgang Schaeuble. Vortraege gehalten auf d. Mitgliederversammmlung d. Inst. Finanzen u. Steuern am 14. April 1988. Vortraege gehalten auf d. Mitgliederversammmlung d. Inst. Finanzen u. Steuern am 14. April 1988

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Assessment issues and new technologies: ePortfolio possibilities

The emergence of new information and communication technologies(ICTs) call for new ways of learning and teaching, and integral to this call is new ways of assessing. This chapter provides insights into how ICT offers educators valuable assessment tools with which to more appropriately assess 21st-century lifelong learnerswho increasingly experience learning in digital, networked learning contexts in which learning involves collaboration and constructing new knowledge. This chapter explores how the interests of learning improvement and accountability can be served using online resources, particularly ePortfolios, and how they can be enhanced by the use of Web 2.0 technologies. Issues and insights are provided through an exploration into how ICT can provide valuable assessment tools for diverse stakeholders, including students, parents, administrators and policy officers