Construction and Convergence of Difference Schemes for a Modell Elliptic Equation with Dirac-delta Function Coefficient
We first discuss the difficulties that arise at the construction of difference schemes on uniform meshes for a specific elliptic interface problem. Estimates for the rate of convergence in discrete energetic Sobolev’s norms compatible with the smoothness of the solution are also presented.
KeywordsTruncation Error Localize Chemical Reaction Uniform Mesh Interface Problem Immerse Boundary Method
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- 1.Li Z.: The Immersed Interface Method-A Numerical Approach for Partial Differential Equations with Interfaces. PhD thesis, University of Washington, 1994.Google Scholar
- 3.Beyer R. P., Leveque R. J.: Analysis of one-dimensional model for the immersed boundary method, SIAM J. Numer. Anal. 29 (1992), 332-364.Google Scholar
- 4.Kandilarov J.: A second-order difference method for solution of diffusion problems with localized chemical reactions. in Finite-Difference methods: Theory and Applications (CFDM 98), Vol. 2, 63–67, Ed. by A. A. Samarskii, P. P. Matus, P. N. Vabishchevich, Inst. of Math., Nat. Acad. of Sci. of Belarus, Minsk 1998.Google Scholar
- 6.Samarskii A. A.: Theory of difference schemes, Nauka, Moscow 1987 (in Russian).Google Scholar
- 7.Samarskii A. A., Lazarov R. D., Makarov V. L.: Difference schemes for differential equations with generalized solutions, Vyshaya Shkola, Moscow 1989 (in Russian).Google Scholar
- 8.Jovanović B. S.: Finite difference method for boundary value problems with weak solutions, Mat. Institut, Belgrade 1993.Google Scholar