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A finite element method using singular functions: interface problems. (English) Zbl 1140.65084

The authors develop solution schemes for interface problems using the finite element method and singular functions. A number of theorems and lemmas for theoretical validation is presented. Some numerical tests are performed which indicate that the \(L_2\) norm accuracy is much better than the theoretical error bound.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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