Optimal Order Error Estimates of a Modified Nonconforming Rotated Q1 IFEM for Interface Problems

Superconvergence Studies of Quadrilateral Nonconforming Rotated Q1 Elements

For the nonconforming rotated Q1 element over a mildly distorted quadrilateral mesh, we propose a superconvergence property at the element center, the vertices and the midpoints of four edges. Numerics are presented to confirm this observation.

A posteriori error estimates for nonconforming finite element methods for fourth-order problems on rectangles

The a posteriori error analysis of conforming finite element discretisations of the biharmonic problem for plates is well established, but nonconforming discretisations are more easy to implement in practice. The a posteriori error analysis for the Morley plate element appears very particular because two edge contributions from an integration by parts vanish simultaneously. This miracle does no...

Optimal a priori estimates for interface problems

A Posteriori Error Estimates for Nonconforming Approximations of Evolutionary Convection-Diffusion Problems

We derive computable upper bounds for the difference between an exact solution of the evolutionary convection-diffusion problem and an approximation of this solution. The estimates are obtained by certain transformations of the integral identity that defines the generalized solution. These estimates depend on neither special properties of the exact solution nor its approximation, and involve on...

A posteriori error estimates for nonconforming approximations of Steklov eigenvalue problems

This paper deals with a posteriori error estimators for the non conforming CrouzeixRaviart finite element approximations of the Steklov eigenvalue problem. First, we define an error estimator of the residual type which can be computed locally from the approximate eigenpair and we prove the equivalence between this estimator and the broken energy norm of the error with constants independent of t...