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hp-DGFEM for nonlinear convection-diffusion problems
Type of publication: Article
Citation:
Publication status: Published
Journal: Mathematics and Computers in Simulation
Volume: 87
Year: 2013
Month: January
Pages: 87-118
DOI: 10.1016/j.matcom.2013.03.001
Abstract: We deal with a numerical solution of nonlinear convection-diffusion problems with the aid of the discontinuous Galerkin finite element method (DGFEM). 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 and it marks mesh elements for a refinement. The regularity indicator decides if the marked elements will be refined by h- or p-technique. The residuum-nonconformity estimator as well as the regularity indicator are easily computable quantities. Moreover, the same technique estimates an algebraic error arising from an iterative solution of the corresponding nonlinear algebraic system. The performance of the proposed hp-DGFEM is demonstrated by five numerical examples.
Preprint project: NCMM
Preprint year: 2013
Preprint number: 10
Preprint ID: NCMM/2013/10
Keywords: Algebraic error, hp-Discontinuous Galerkin finite element method, Regularity estimator, Residuum-nonconformity indicator
Authors Dolejší, Vít
Added by: [JP]
Total mark: 0
Attachments
  • Dolejsi_all.pdf
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