A Weakly Over-Penalized Non-Symmetric Interior Penalty Method

Date of Online Publication: 14/04/2007
Keywords: interior penalty methods, weakly over-penalized, preconditioner, quasi-optimal error estimates
Authors: Susanne C. Brenner, Luke Owens
Pages: 35-48
A weakly over-penalized nonsymmetric interior penalty method for second order elliptic boundary value problems is considered in this paper. This method is consistent, stable for any choice of the penalty parameter and satisfies quasi-optimal error estimates in both the energy norm and the L2 norm. Furthermore, there exists a simple block diagonal preconditioner that keeps the condition number of the discrete problem at the order of O(h-2). Both theoretical and numerical results are presented.


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