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.

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Key words

symmetric interior penalty method, weak over-penalization

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