Inverse-average-type finite element discretizations of selfadjoint second-order elliptic problems

Inverse-Average-Type Finite Element Discretizations of Selfadjoint Second-Order Elliptic Problems

This paper is concerned with the analysis of a class of "special purpose" piecewise linear finite element discretizations of selfadjoint second-order elliptic boundary value problems. The discretization differs from standard finite element methods by inverse-average-type approximations (along element sides) of the coefficient function a(x) in the operator — div(a(x) grad u). The derivation of t...

Multilevel Approaches to Nonconforming Finite Element Discretizations of Linear Second Order Elliptic Boundary Value Problems

We consider adaptive multilevel techniques for nonconforming nite element dis-cretizations of second order elliptic boundary value problems. In particular, we will focus on two basic ingredients of an eecient adaptive algorithm. The rst one is the iterative solution of the arising linear system by preconditioned conjugate gradient methods and the second one is an a posteriori error estimator fo...

Mortar Finite Volume Element Approximations of Second Order Elliptic Problems

A Finite Element Method for Second Order Nonvariational Elliptic Problems

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solvin...

Boundary preconditioners for mixed finite-element discretizations of fourth-order elliptic problems

Abstract We extend the preconditioning approach of Glowinski and Pironneau, and of Peisker to the case of mixed finite element general fourth-order elliptic problems. We show that H−1/2-preconditioning on the boundary leads to mesh-independent performance of iterative solvers of Krylov subspace type. In particular, we show that the field of values of the boundary Schur complement preconditioned...