Discontinuous Galerkin method Stability Error estimates Analytical solutions Test-functions Mixed discretisation methods for the Discontinuous Galerkin method with analytical test-functions. Juergen Geiser Geiser Juergen Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 30 pp.

Mixed discretisation methods for the Discontinuous Galerkin method with analytical test-functions.

Juergen Geiser

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 30 pp.

MSC 2000

65N12 Stability and convergence of numerical methods
65N15 Error bounds

Abstract
The idea to this paper is a framework for modifying a standard Discontinuous Galerkin method for convection-diffusion-reaction-equations. We develop an abstract theory for the stability and error-estimates in $L^2$-norms for a mixed formulation. For diverse test-functions we apply our abstract theory. We apply the theory for the test-functions coming from analytical solutions of the adjoint problem. With the new test-functions we could improve the approximation. At the end we discuss the application of the new analytical test-functions.

This document is well-formed XML.