A Numerical Study of a Singular Elliptic Boundary Value Problem

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Abstract
Finite element and finite difference methods for the solution of singular boundary value problems are compared using a model problem arising in fluid dynamics. It is shown that when finite difference equations are “matched” with the local behaviour of the solution near the singularity they can be competitive with existing finite element approximations based on piecewise bilinear functions supplemented with suitable singular terms. A significant improvement in the latter is shown to be possible by careful construction of the singular term.

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