Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates

Residual and Hierarchical a Posteriori Error Estimates for Nonconforming Mixed Finite Element Methods

We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Fi...

Postprocessing Mixed Finite Element Methods For Solving Cahn-Hilliard Equation: Methods and Error Analysis

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which man...

Localized pointwise error estimates for mixed finite element methods

In this paper we give weighted, or localized, pointwise error estimates which are valid for two different mixed finite element methods for a general second-order linear elliptic problem and for general choices of mixed elements for simplicial meshes. These estimates, similar in spirit to those recently proved by Schatz for the basic Galerkin finite element method for elliptic problems, show tha...

A Posteriori Error Estimates for Nonconforming Finite Element Schemes

We derive a posteriori error estimates for nonconforming discretizations of Poisson's and Stokes' equations. The estimates are residual based and make use of weight factors obtained by a duality argument. Crouzeix-Raviart elements on triangles and rotated bilinear elements are considered. The quadrilateral case involves the introduction of additional local trial functions. We show that their in...

A new a priori error analysis of nonconforming and mixed finite element methods