Convergence of adaptive discontinuous Galerkin methods
Copyright policy )Convergence of adaptive discontinuous Galerkin methods
We develop a general convergence theory for adaptive discontinu- ous Galerkin methods for elliptic PDEs covering the popular SIPG, NIPG and LDG schemes as well as all practically relevant marking strategies. Another key feature of the presented result is, that it holds for penalty parameters only necessary for the standard analysis of the respective scheme. The analysis is based on a quasi interpolation into a newly developed limit space of the adaptively created non-conforming discrete spaces, which enables to generalise the basic convergence result for conforming adaptive finite element methods by Morin, Siebert, and Veeser [A basic convergence result for conforming adaptive finite elements, Math. Models Methods Appl. Sci., 2008, 18(5), 707–737].
Ergebnisberichte des Instituts für Angewandte Mathematik;575
- TU Dortmund University Germany
- Ruhr University Bochum Germany
- National Technical University of Athens Greece
- University of Leicester United Kingdom
convergence, Error bounds for boundary value problems involving PDEs, adaptive discontinuous Galerkin methods, 610, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, elliptic problems, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, info:eu-repo/classification/ddc/610
convergence, Error bounds for boundary value problems involving PDEs, adaptive discontinuous Galerkin methods, 610, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, elliptic problems, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, info:eu-repo/classification/ddc/610
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