EuDML | Browse

Page 1

Displaying 1 – 6 of 6

Variational approximation of flux in conforming finite element methods for elliptic partial differential equations : a model problem

Franco Brezzi, Thomas J. R. Hughes, Endre Süli (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We consider the approximation of elliptic boundary value problems by conforming finite element methods. A model problem, the Poisson equation with Dirichlet boundary conditions, is used to examine the convergence behavior of flux defined on an internal boundary which splits the domain in two. A variational definition of flux, designed to satisfy local conservation laws, is shown to lead to improved rates of convergence.

Variational formulation and analysis of a linearized 2-D model with no axial symmetry for a two-phase water-petroleum flow.

Angulo, W., López, H. (2008)

Divulgaciones Matemáticas

Variational Principles and Convergence of Finite Element Approximations of a Holonomic Elastic-Plastic Problem.

B.D. Reddy, T.B. Griffin (1987/1988)

Numerische Mathematik

Variational problems in domains with cusp points

Alexander Ženíšek (1993)

Applications of Mathematics

The finite element analysis of linear elliptic problems in two-dimensional domains with cusp points (turning points) is presented. This analysis needs on one side a generalization of results concerning the existence and uniqueness of the solution of a constinuous elliptic variational problem in a domain the boundary of which is Lipschitz continuous and on the other side a presentation of a new finite element interpolation theorem and other new devices.

Variational sensitivity analysis of parametric Markovian market models

Norbert Hilber, Christoph Schwab, Christoph Winter (2008)

Banach Center Publications

Parameter sensitivities of prices for derivative contracts play an important role in model calibration as well as in quantification of model risk. In this paper a unified approach to the efficient numerical computation of all sensitivities for Markovian market models is presented. Variational approximations of the integro-differential equations corresponding to the infinitesimal generators of the market model differentiated with respect to the model parameters are employed. Superconvergent approximations...

Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method

A. Klöckner, T. Warburton, J. S. Hesthaven (2011)

Mathematical Modelling of Natural Phenomena

We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG) methods. The output of this detector is a reliably scaled, element-wise smoothness estimate which is suited as a control input to a shock capture mechanism. Using an artificial viscosity in the latter role, we obtain a DG scheme for the numerical solution of nonlinear systems of conservation laws. Building on work by Persson and Peraire, we thoroughly justify the...