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A finite element method for domains with corners. (English) Zbl 0768.73072
A new finite element method is devised for the numerical solution of elliptic boundary value problems with geometrical singularities. In it, the singularity is eliminated from the computational domain in an exact fashion. This is in contrast to other common methods, such as those which use a refined mesh in the singularity region, or those which use special singular finite elements. In them, the singularity is treated as a part of the numerical scheme. The new method is illustrated on an elliptic differential equation in a domain containing a re-entrant corner.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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