hp-Adaptive Discontinuous Galerkin Finite Element Methods for First-Order Hyperbolic Problems
- 1 January 2001
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing
- Vol. 23 (4) , 1226-1252
- https://doi.org/10.1137/s1064827500378799
Abstract
We consider the a posteriori error analysis of hp-discontinuous Galerkin finite element approximations to first-order hyperbolic problems. In particular, we discuss the question of error estimation for linear functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local polynomial-degree variation and local mesh subdivision. The theoretical results are illustrated by a series of numerical experimentsKeywords
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