Abstract
Finite element methods, using bilinear basis functions supplemented by singular functions, are described for solving elliptic boundary value problems with corner singularities: The procedure of mesh refinement in the finite element method in the neighborhood of a singularity is illustrated with respect to the harmonic mixed boundary value problem of the slit. Numerical results obtained right up to the tip of the slit are compared at selected points in the field with values obtained by dual series and finite difference methods.
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