A Simple Finite Element Method for Non-divergence Form Elliptic Equations

Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations with Cordès Coefficients

Abstract. Non-divergence form elliptic equations with discontinuous coefficients do not generally posses a weak formulation, thus presenting an obstacle to their numerical solution by classical finite element methods. We propose a new hp-version discontinuous Galerkin finite element method for a class of these problems that satisfy the Cordès condition. It is shown that the method exhibits a co...

Buckling Analysis of Rectangular Functionally Graded Plates with an Elliptic Hole Under Thermal Loads

This paper presents thermal buckling analysis of rectangular functionally graded plates (FG plates) with an eccentrically located elliptic cutout. The plate governing equations derived by the first order shear deformation theory (FSDT) and finite element formulation is developed to analyze the plate behavior subjected to a uniform temperature rise across plate thickness. It is assumed that the ...

Mixed Finite Element Methods for Hamilton-Jacobi-Bellman Type Equations

The numerical solution of Dirichlet's problem for a second order elliptic operator in divergence form with arbitrary nonlinearities in the rst and zero order terms is considered. The mixed nite element method is used. Existence and uniqueness of the approximation are proved and optimal error estimates in L are demonstrated for the relevant functions. Error estimates are also derived in L, 2 q +...

Hodge decomposition for divergence-free vector fields and two-dimensional Maxwell's equations

We propose a new numerical approach for two-dimensional Maxwell's equations that is based on the Hodge decomposition for divergence-free vector fields. In this approach an approximate solution for Maxwell's equations can be obtained by solving standard second order scalar elliptic boundary value problems. This new approach is illustrated by a P 1 finite element method.

CONVERGENCE ANALYSIS OF FINITE ELEMENT METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS IN NON-DIVERGENCE FORM by