Graded mesh approximation in weighted Sobolev spaces and elliptic equations in 2D

GRADED MESH APPROXIMATION IN WEIGHTED SOBOLEV SPACES AND ELLIPTIC EQUATIONS IN 2D By

We study the approximation properties of some general finiteelement spaces constructed using improved graded meshes. In our results, either the approximating function or the function to be approximated (or both) are in a weighted Sobolev space. The finite-element spaces that we define are obtained from conformally invariant families of finite elements (no affine invariance is used), stressing t...

Graded mesh approximation in weighted Sobolev spaces and elliptic equations in 2D

We study the approximation properties of some general finiteelement spaces constructed using improved graded meshes. In our results, either the approximating function or the function to be approximated (or both) are in a weighted Sobolev space. The finite-element spaces that we define are obtained from conformally invariant families of finite elements (no affine invariance is used), stressing t...

Weighted Sobolev Spaces and Degenerate Elliptic Equations

In the case ω = 1, this space is denoted W (Ω). Sobolev spaces without weights occur as spaces of solutions for elliptic and parabolic partial differential equations. In various applications, we can meet boundary value problems for elliptic equations whose ellipticity is “disturbed” in the sense that some degeneration or singularity appears. This “bad” behaviour can be caused by the coefficient...

Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

A Priori Estimates for Elliptic Equations in Weighted Sobolev Spaces

In this paper we prove some a priori bounds for the solutions of the Dirichlet problem for elliptic equations with singular coefficients in weighted Sobolev spaces. Mathematics subject classification (2010): 35J25, 35B45, 35R05.