Optimal convergence analysis of an immersed interface finite element method. (English) Zbl 1198.65212
Authors’ abstract: We analyze an immersed interface finite element method based on linear polynomials on noninterface triangular elements and piecewise linear polynomials on interface triangular elements. The flux jump condition is weakly enforced on the smooth interface. Optimal error estimates are derived in the broken \(H ^{1}\)-norm and \(L ^{2}\)-norm.
Reviewer: Dietrich Braess (Bochum)
MSC:
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
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