Thomas Lewis
Abstract:
The goal of this article is to explore and motivate stabilization requirements
for various types of discontinuous Galerkin (DG) methods.
A new approach for the understanding of DG approximation methods for second
order elliptic partial differential equations is introduced.
The approach explains the weaker stability requirements for local
discontinuous Galerkin (LDG) methods when compared to interior-penalty
discontinuous Galerkin methods while also motivating the existence of methods
such as the minimal dissipation LDG method that are stable without the addition
of interior penalization. The main idea is to relate the underlying DG gradient
approximation to distributional derivatives instead of the traditional
piecewise gradient operator associated with broken Sobolev spaces.
Published March 21, 2016.
Math Subject Classifications: 65J02, 65N02, 35C02.
Key Words: Discontinuous Galerkin methods; broken Sobolev spaces;
distributional derivatives; numerical derivatives.
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Thomas Lewis Department of Mathematics and Statistics The University of North Carolina at Greensboro Greensboro, NC 27412, USA email: tllewis3@uncg.edu |
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