The L2-Optimality of the IIPG Method for Odd Degrees of Polynomial Approximation in 1D

Authors:
Vít Dolejší;Oto Havle
Affiliations:
Faculty of Mathematics and Physics, Charles University Prague, Prague 8, Czech Republic 186-75;Faculty of Mathematics and Physics, Charles University Prague, Prague 8, Czech Republic 186-75
Venue:
Journal of Scientific Computing
Year:
2010

Citing 6
Cited 1

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Poincaré-Friedrichs Inequalities for Piecewise H1 Functions

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Sub-optimal Convergence of Non-symmetric Discontinuous Galerkin Methods for Odd Polynomial Approximations

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Some nonstandard error analysis of discontinuous Galerkin methods for elliptic problems

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Abstract

The paper deals with a numerical analysis of the incomplete interior penalty Galerkin (IIPG) method applied to one dimensional Poisson problem. Based on a particular choice of the interior penalty parameter 驴 (order of O(h 驴1)), we derive the optimal error estimate in the L 2-norm for odd degrees of polynomial approximation for locally quasi-uniform meshes. Moreover, we show that only the mentioned choice of the penalty parameter leads to optimal orders of convergence. Finally, presented numerical experiments verify the theoretical results.