Boluchevskaya A.V. Piecewise smooth approximation for elliptic systems solutions

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Boluchevskaya Anna Vladimirovna
 
Post-Graduate Student, Assistant Teacher, Chair of Computer Science and Experimental Mathematics, Volgograd State University
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Prospect Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. The paper is devoted to the problem of piecewise smooth approximation for elliptic system solutions defined on triangular grids. It is shown that when we approximate a differential of such a solution by the differential of the approximating mapping the error depends on the triangles shapes and sizes. A mapping is build to approximate the differential with the error that does not depend on triangles in the grid. The analogous results are obtained for Beltrami equation solutions.

Key words: piecewise smooth approximation, approximation of a differential, elliptic system of equations, Beltrami equation, approximation error bound, triangulation.

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Piecewise smooth approximation for elliptic systems solutions by Boluchevskaya A.V. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №2 (15) 2011 pp. 4-16

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