hp-discontinuous Galerkin method for nonlinear problems

• ID: 2653, RIV: 10128846
• ISSN: 1803-9782, ISBN: not specified
• source: ACC Journal
• keywords: hp-discontinuous Galerkin method; nonlinear boundary value problems
• authors: Vít Dolejší
• authors from KNM: Dolejší Vít

Abstract

We deal with a numerical solution of nonlinear convection-diffusion problems with the aid of the discontinuous Galerkin finite element (DGFE) method. We propose a new $hp$-adaptation technique, which is based on a combination of a residuum-nonconformity estimator and a regularity indicator. The residuum-nonconformity estimator consists of two building blocks (residuum error indicator and the value of the nonconformity). The estimator marks mesh elements for a refinement. The regularity indicator decides if the marked elements will be refined by h- or p-technique.