Volume 30, pp. 107-127, 2008.

A weakly over-penalized symmetric interior penalty method

Susanne C. Brenner, Luke Owens, and Li-Yeng Sung

Abstract

We introduce a new symmetric interior penalty method for symmetric positive definite second order elliptic boundary value problems, where the jumps across element boundaries are weakly over-penalized. Error estimates are derived in the energy norm and the $L_2$ norm for both conforming and nonconforming meshes. Numerical results illustrating the performance of the method are also presented.

Full Text (PDF) [426 KB]

Key words

symmetric interior penalty method, weak over-penalization

AMS subject classifications

65N30

Links to the cited ETNA articles

[9]Vol. 18 (2004), pp. 42-48 Susanne C. Brenner: Discrete Sobolev and Poincaré inequalities for piecewise polynomial functions

ETNA articles which cite this article

Vol. 37 (2010), pp. 214-238 Susanne C. Brenner, Thirupathi Gudi, and Li-Yeng Sung: A weakly over-penalized symmetric interior penalty method for the biharmonic problem
Vol. 46 (2017), pp. 190-214 Susanne C. Brenner, Eun-Hee Park, and Li-Yeng Sung: A BDDC preconditioner for a symmetric interior penalty Galerkin method

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