A Priori and a Posteriori Error Estimates of a Weakly Over-Penalized Interior Penalty Method for Non-Self-Adjoint and Indefinite Problems

Abstract

In this paper, we study a weakly over-penalized interior penalty method for non-self-adjoint and indefinite problems. An optimal a priori error estimate in the energy norm is derived. In addition, we introduce a residual-based a posteriori error estimator, which is proved to be both reliable and efficient in the energy norm. Some numerical tests are presented to validate our theoretical analysis.