A priori error estimation of finite element models from first principles

A priori error estimation for the dual mixed finite element method of the elastodynamic problem in a polygonal domain, II

In this paper we analyze a new dual mixed formulation of the elastodynamic system in polygonal domains. In this formulation the symmetry of the strain tensor is relaxed by the rotational of the displacement. For the time discretization of this new dual mixed formulation, we use an explicit scheme. After the analysis of stability of the fully discrete scheme, L∞ in time, L2 in space a priori err...

A Priori Error Estimate of a Multiscale Finite Element Method for Transport Modeling

This work proposes an a priori error estimate of a multiscale finite element method to solve convection-diffusion problems where both velocity and diffusion coefficient exhibit strong variations at a scale which is much smaller than the domain of resolution. In that case, classical discretization methods, used at the scale of the heterogeneities, turn out to be too costly. Our method, introduce...

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

A Posteriori Finite Element Error Estimation for Diffusion Problems

Adjerid et al. 2] and Yu 19, 20] show that a posteriori estimates of spatial discretiza-tion errors of piecewise bi-p polynomial nite element solutions of elliptic and parabolic problems on meshes of square elements may be obtained from jumps in solution gradients at element vertices when p is odd and from local elliptic or parabolic problems when p is even. We show that these simple error esti...