Galerkin methods for singular boundary value problems in one space dimension

Galerkin Methods for Singular Boundary Value Problems in One Space Dimension

Two Galerkin type piecewise polynomial approximation procedures based on bilinear forms with different weight functions are analyzed and compared. Optimal order error estimates are proved and numerical results are presented.

Convergence Analysis for a Nonsymmetric Galerkin Method for a Class of Singular Boundary Value Problems in One Space Dimension

For the method and problems under consideration we estimate the error in the maximum norm as well as at individual nodal points. In order to obtain full superconvergence at all nodal points we have to introduce local mesh refinements, even though the exact solution is smooth for the given class of problems.

Boundary Value Problems in One Dimension

While its roots are firmly planted in the finite-dimensional world of matrices and vectors, the full scope of linear algebra is much broader. Its historical development and, hence, its structures, concepts, and methods, were strongly influenced by linear analysis — specifically, the need to solve linear differential equations, linear boundary value problems, linear integral equations, and the l...

Existence and Uniqueness of Solutions for Boundary Value Problems to the Singular One-Dimension p-Laplacian

Discontinuous Galerkin Methods for Periodic Boundary Value Problems

This article considers the extension of well-known discontinuous Galerkin (DG) finite element formulations to elliptic problems with periodic boundary conditions. Such problems routinely appear in a number of applications, particularly in homogenization of composite materials. We propose an approach in which the periodicity constraint is incorporated weakly in the variational formulation of the...