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Nitsche-type finite element method for elliptic problems with singularities

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • B. Heinrich

    (Technische Universität Chemnitz)

Abstract

Summary The paper deals with a Nitsche-type finite element method for treating non-matching meshes at the interface of a domain decomposition. This method is applied to transmission (or interface) problems with discontinuous coefficients, where the polygonal boundary of the plane domain and the polygonal interface cause singularities in the solution. In a natural way, the interface of the transmission problem is taken as the interface of the domain decomposition and of the non-matching meshes. Properties of the Nitsche-type finite element scheme and error estimates are given when the solution has a low degree of regularity. For appropriate local mesh refinement, optimal convergence rates as known for the classical finite element method and regular solution are obtained. Numerical tests illustrate the approach and confirm the theoretical results.

Suggested Citation

  • B. Heinrich, 2003. "Nitsche-type finite element method for elliptic problems with singularities," Springer Books, in: Franco Brezzi & Annalisa Buffa & Stefania Corsaro & Almerico Murli (ed.), Numerical Mathematics and Advanced Applications, pages 837-845, Springer.
    • Handle: RePEc:spr:sprchp:978-88-470-2089-4_76
    DOI: 10.1007/978-88-470-2089-4_76
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