Interpolation, projection and hierarchical bases in discontinuous Galerkin methods
Lutz Angermann, Christian Henke
TL;DR
This paper investigates advanced interpolation, projection, and hierarchical basis techniques in discontinuous Galerkin methods, providing error estimates and inverse inequalities with applications to discrete conservation laws.
Contribution
It introduces new error estimates and inverse inequalities for polynomial approximations using hierarchical bases in discontinuous Galerkin methods, focusing on applications to conservation laws.
Findings
Error estimates for quadrature and projection operators
Inverse inequalities for hierarchical bases
Applications to discrete conservation laws
Abstract
The paper presents results on piecewise polynomial approximations of tensor product type in Sobolev-Slobodecki spaces by various interpolation and projection techniques, on error estimates for quadrature rules and projection operators based on hierarchical bases, and on inverse inequalities. The main focus is directed to applications to discrete conservation laws.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Probabilistic and Robust Engineering Design · Numerical methods in engineering