A Posteriori Error Estimates of a Weakly Over-Penalized Symmetric Interior Penalty Method for Elliptic Eigenvalue Problems

A weakly over-penalized symmetric interior penalty method is applied to solve elliptic eigenvalue problems. We derive a posteriori error estimator of residual type, which proves to be both reliable and efficient in the energy norm. Some numerical tests are provided to confirm our theoretical analysis.

ConstrainedC0Finite Element Methods for Biharmonic Problem

This paper presents some constrainedC0finite element approximation methods for the biharmonic problem, which include theC0symmetric interior penalty method, theC0nonsymmetric interior penalty method, and theC0nonsymmetric superpenalty method. In the finite element spaces, theC1continuity across the interelement boundaries is obtained weakly by the constrained condition. For theC0symmetric interior penalty method, the optimal error estimates in the brokenH2norm and in theL2norm are derived. However, for theC0nonsymmetric interior penalty method, the error estimate in the brokenH2norm is optimal and the error estimate in theL2norm is suboptimal because of the lack of adjoint consistency. To obtain the optimalL2error estimate, theC0nonsymmetric superpenalty method is introduced and the optimalL2error estimate is derived.