On Some Convergence Properties for Finite Element Approximations to the Inverse of Linear Elliptic Operators

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations

It is shown that the Ritz projection onto spaces of piecewise linear finite elements is bounded in the Sobolev space, Wp\ for 2 <p < oo. This implies that for functions in W¿ n Wp the error in approximation behaves like 0(h) in Wx, for 2 <p =c oo, and like 0(h2) in Lp, for 2 *íp < oo. In all these cases the additional logarithmic factor previously included in error estimates for linear finite e...

Convergence Analysis for Eigenvalue Approximations on Triangular Finite Element Meshes

The paper is devoted to the eigenvalue problem for a second order strongly elliptic operator. The problem is considered on curved domains, which require interpolated boundary conditions in approximating finite element formulation. The necessary triangulations for solving the eigenvalue problem consists of isoparametric elements of degree n, where n is any integer greater than two. An approximat...

Convergence of the discrete free boundaries for finite element approximations

Error Estimates for Finite Element Approximations of Elliptic Control Problems

We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.