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Chang, Kwang S.; Kwak, D. Y.

Discontinuous bubble scheme for elliptic problems with jumps in the solution. (English) Zbl 1225.65109

Comput. Methods Appl. Mech. Eng. 200, No. 5-8, 494-508 (2011).
Summary: We propose a new numerical method to solve an elliptic problem with jumps both in the solution and derivative along an interface. By considering a suitable function which has the same jumps as the solution, we transform the problem into one without jumps. Then we apply the immersed finite element method in which we allow uniform meshes so that the interface may cut through elements to discretize the problem. Some convenient way of approximating the jumps of the solution by piecewise linear functions is suggested. Our method can also handle the case when the interface passes through grid points. We believe this paper presents the first resolution of such cases. Numerical experiments for various problems show second-order convergence in \(L^{2}\) and first order in \(H^{1}\)-norms. Moreover, the convergence order is very robust for all problems tested.

Cited in 3 Reviews
Cited in 23 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

jumps in the solution; discontinuous bubble; immersed interface; immersed finite element method; uniform grid; robust convergence
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References:

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