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Finite element methods for semilinear elliptic problems with smooth interfaces

Author

Listed:
  • Bhupen Deka

    (Tezpur University)

  • Tazuddin Ahmed

    (Tezpur University)

Abstract

The purpose of this paper is to study the finite element method for second order semilinear elliptic interface problems in two dimensional convex polygonal domains. Due to low global regularity of the solution, it seems difficult to achieve optimal order of convergence with straight interface triangles [Numer. Math., 79 (1998), pp. 175–202]. For a finite element discretization based on a mesh which involve the approximation of the interface, optimal order error estimates in L 2 and H 1-norms are proved for linear elliptic interface problem under practical regularity assumptions of the true solution. Then an extension to the semilinear problem is also considered and optimal error estimate in H 1 norm is achieved.

Suggested Citation

  • Bhupen Deka & Tazuddin Ahmed, 2011. "Finite element methods for semilinear elliptic problems with smooth interfaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 42(4), pages 205-223, August.
    • Handle: RePEc:spr:indpam:v:42:y:2011:i:4:d:10.1007_s13226-011-0014-8
    DOI: 10.1007/s13226-011-0014-8
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    Cited by:

    1. B. Deka & R. C. Deka, 2013. "Finite element method for a class of parabolic integro-differential equations with interfaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(6), pages 823-847, December.

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