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

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

Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods

We derive in this paper a unified framework for a priori and a posteriori error analysis of mixed finite element discretizations of second-order elliptic problems. It is based on the classical primal weak formulation, the postprocessing of the potential proposed in [T. Arbogast and Z. Chen, On the implementation of mixed methods as nonconforming methods for secondorder elliptic problems, Math. ...

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...

A Priori and A Posteriori Pseudostress-velocity Mixed Finite Element Error Analysis for the Stokes Problem

The pseudostress-velocity formulation of the stationary Stokes problem allows a Raviart-Thomas mixed finite element formulation with quasi-optimal convergence and some superconvergent reconstruction of the velocity. This local postprocessing gives rise to some averaging a posteriori error estimator with explicit constants for reliable error control. Standard residual-based explicit a posteriori...

Numerical analysis and a-posteriori error control for a new nonconforming linear finite element on quadrilaterals

Starting with a short introduction of the new nonconforming linear quadrilateral P̃1-finite element which has been recently proposed by Park ([13, 14]), we examine in detail the numerical behaviour of this element with special emphasis on the treatment of Dirichlet boundary conditions, efficient matrix assembly, solver aspects and the use as Stokes element in CFD. Furthermore, we compare the num...