A new symmetric local projection method built on residual bases (RELP) makes linear equal-order finite element pairs stable for the Darcy problem. The derivation is performed inside a Petrov-Galerkin enriching space approach (PGEM) which indicates parameter-free terms to be added to the Galerkin method without compromising consistency. Velocity and pressure spaces are augmented using solutions ...

This article introduces and analyzes a weak Galerkin mixed finite element method for solving the biharmonic equation. The weak Galerkin method, first introduced by two of the authors (J. Wang and X. Ye) in [52] for second order elliptic problems, is based on the concept of discrete weak gradients. The method uses completely discrete finite element functions and, using certain discrete spaces an...

Article history: Received 27 January 2014 Received in revised form 22 October 2014 Accepted 26 October 2014 Available online 30 October 2014

Article history: Received 22 November 2012 Received in revised form 13 June 2014 Accepted 1 July 2014 Available online 8 July 2014

A posteriori error estimation for conforming, non-conforming and discontinuous finite element schemes are discussed within a single framework. By dealing with three ostensibly different schemes under the same umbrella, the same common underlying principles at work in each case are highlighted leading to a clearer understanding of the issues involved. The ideas are presented in the context of pi...

This paper presents a Galerkin-based meshless method for calculating stress-intensity factors (SIFs) for a stationary crack in two-dimensional functionally graded materials of arbitrary geometry. The method involves an element-free Galerkin method (EFGM), where the material properties are smooth functions of spatial coordinates and two newly developed interaction integrals for mixed-mode fractu...