A Priori and a Posteriori Error Estimates of a Weakly Over-Penalized Interior Penalty Method for Non-Self-Adjoint and Indefinite Problems (Journal of Computational Mathematics, 2018)
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.
Keywords: Interior penalty method; Weakly over-penalization; Non-self-adjoint and indefinite; A priori error estimate; A posteriori error estimate.