In this paper, we first split the biharmonic equation !2u = f with nonhomogeneous essential boundary conditions into a system of two second order equations by introducing an auxiliary variable v = !u and then apply an hp-mixed discontinuous Galerkin method to the resulting system. The unknown approximation vh of v can easily be eliminated to reduce the discrete problem to a Schur complement sys...

A computable error bound for mixed finite element methods is established in the model case of the Poisson–problem to control the error in the H(div,Ω) ×L2(Ω)–norm. The reliable and efficient a posteriori error estimate applies, e.g., to Raviart–Thomas, Brezzi-Douglas-Marini, and Brezzi-DouglasFortin-Marini elements. 1. Mixed method for the Poisson problem Mixed finite element methods are well-e...

We develop a mixed finite element method for elliptic problems on hexahedral grids that reduces to cell-centered finite differences. The paper is an extension of our earlier paper for quadrilateral and simplicial grids [M. F. Wheeler and I. Yotov, SIAM J. Numer. Anal., 44 (2006), pp. 2082–2106]. The construction is motivated by the multipoint flux approximation method, and it is based on an enh...

A mixed variational formulation of the Brinkman problem is presented which is uniformly well–posed for degenerate (vanishing) coefficients under the hypothesis that a generalized Poincaré inequality holds. The construction of finite element schemes which inherit this property is then considered.

We propose a multilevel preconditioning strategy for the iterative solution of large sparse linear systems arising from a nite element discretization of the radiation di usion equations. In particular, these equations are solved using a mixed nite element scheme in order to make the discretization discontinuous, which is imposed by the application in which the di usion equation will be embedded...

This paper describes a numerical solution for plane elasticity problem. It includes algorithms for discretization by mixed finite element methods. The discrete scheme allows the utilization of Brezzi Douglas Marini element (BDM1) for the stress tensor and piecewise constant elements for the displacement. The numerical results are compared with some previously published works or with others comi...

A nonconforming mixed finite element method for nonlinear hyperbolic equations is discussed. Existence and uniqueness of the solution to the discrete problem are proved. Priori estimates of optimal order are derived for both the displacement and the stress.

An adaptive mixed finite element method (AMFEM) is designed to guarantee an error reduction, also known as saturation property: after each refinement step, the error for the fine mesh is strictly smaller than the error for the coarse mesh up to oscillation terms. This error reduction property is established here for the Raviart–Thomas finite element method with a reduction factor ρ < 1 uniforml...