A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e590" altimg="si3.svg"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:math> finite element approximation of planar oblique derivative problems in non-divergence form

Oblique derivative problem for elliptic equations in non-divergence form with VMO coefficients

A priori estimates and strong solvability results in Sobolev space W 2,p(Ω), 1 < p < ∞ are proved for the regular oblique derivative problem 8<: Pni,j=1 aij(x) ∂u ∂xi∂xj = f(x) a.e. Ω ∂u ∂l + σ(x)u = φ(x) on ∂Ω when the principal coefficients aij are VMO ∩ L∞ functions.

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

Analysis of Finite Element Approximation of Evolution Problems in Mixed Form

Abstract. This paper deals with the finite element approximation of evolution problems in mixed form. Following [8], we handle separately two types of problems. A model for the first case is the heat equation in mixed form, while the time dependent Stokes problem fits within the second one. For either case, we give sufficient conditions for a good approximation in the natural functional spaces....

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

We develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. Also general meshes with polytopal element and hanging node can be used in the method. We prove that our finit...

Finite element approximation for a class of parameter estimation problems

In this paper, we study adaptive finite element discretisation schemes for a class of parameter estimation problem. We propose to use adaptive multi-meshes in developing efficient algorithms for the estimation problem. We derive equivalent a posteriori error estimators for both the state and the control approximation, which particularly suit an adaptive multi-mesh finite element scheme. The err...