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Galerkin boundary element method for Dirichlet problem of 2D heat conduction. (Chinese. English summary) Zbl 1212.65361

Summary: The Dirichlet problem of the two-dimensional heat conduction equation is considered. By adopting the time-dependent fundamental solution, an indirect boundary integral equation and its equivalent Galerkin variational formula which is based on simple layer potential, a solution for the equation is obtained. The method is involved with quadruple integral calculation on space-time. Under the condition that the equation is discretized by adopting a constant cell, the integral formulas needed by actualizing a numerical calculation are deduced. Finally, numerical examples are given to illustrate the feasibility and the efficiency of the proposed method.

MSC:

65M38 Boundary element methods for initial value and initial-boundary value problems involving PDEs
80M15 Boundary element methods applied to problems in thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
35K05 Heat equation
65M80 Fundamental solutions, Green’s function methods, etc. for initial value and initial-boundary value problems involving PDEs
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