Finite element methods for semilinear elliptic problems with smooth interfaces |
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Authors: | Bhupen Deka Tazuddin Ahmed |
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Institution: | 1.Department of Mathematical Sciences,Tezpur University,Tezpur,India |
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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. |
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Keywords: | |
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