Quasi-Interpolation and A Posteriori Error Analysis in 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. ...

A Posteriori Error Analysis and Adaptive Finite Element Methods for Electromagnetic and Acoustic Problems

A posteriori error analysis of hp-version discontinuous Galerkin finite-element methods for second-order quasi-linear elliptic PDEs

We develop the a posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finiteelement methods for a class of second-order quasi-linear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh dependent) energy norm. The bounds are explicit in the local mesh size and the local polynomial degree of the...

Recent Advances of a Posteriori Error Analysis and Adaptive Finite Element Methods

Recent Progress on A-posteriori Error Analysis for the p and h-p Finite Element Methods

This paper investigates recent progress on a-posteriori error analysis for the high-order finite element method(FEM). The paper will discuss the differences between a-posteriori error estimations for lower-order FEM and those for high-order FEM, and analyzes the technical and methodological differences on a-posteriori error estimations for high-order FEM in one dimension and in high dimensions....