Parallel finite element analysis for hyperbolic problems

Analysis of Finite Element Methods for Linear Hyperbolic Problems

We summarize several techniques of analysis for finite element methods for linear hyperbolic problems, illustrating their key properties on the simplest model problem. These include the discontinuous Galerkin method, the continuous Galerkin methods on rectangles and triangles, and a nonconforming linear finite element on a special triangular mesh.

Discontinuous Galerkin finite element methods for second order hyperbolic problems

In this paper, we prove a priori and a posteriori error estimates for a finite element method for linear second order hyperbolic problems (linear wave equations) based on using spacetime finite element discretizations (for displacements and displacement velocities) with (bilinear) basis functions which are continuous in space and discontinuous in time. We refer to methods of this form as discon...

Hp-finite Element Methods for Hyperbolic Problems A

This paper is devoted to the a priori and a posteriori error analysis of the hp-version of the discontinuous Galerkin nite element method for partial differential equations of hyperbolic and nearly-hyperbolic character. We consider second-order partial diierential equations with nonnegative characteristic form, a large class of equations which includes convection-dominated diiusion problems , d...

A Posteriori Error Analysis And Adaptivity For Finite Element Approximations Of Hyperbolic Problems

A posteriori error analysis and adaptivity for nite element approximations of hyperbolic problems a Endre S uli The aim of this article is to present an overview of recent developments in the area of a posteriori error estimation for nite element approximations of hyperbolic problems. The approach pursued here rests on the systematic use of hyperbolic duality arguments. We also discuss the ques...

Parallel Adaptive Finite Element Methods for Problems in Natural Convection