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A 66 line heat transfer finite element code to highlight the dual approach. (English) Zbl 1443.65192

Summary: The paper presents a compact Matlab implementation of a finite element code performing dual analysis of heat conduction problems. After a short presentation of the concerned variational principles, the conductivity matrices of the dual models are developed explicitly. In the next step, a Matlab procedure is written. It shows in 66 statements how it is possible to perform the dual analysis using the unique formalism based on a global conductivity matrix. This fully general method allows using the same finite element code to run the dual analyses. After showing the convergence properties, a second application is developed in order to show how easily the code can be modified. The last part of the paper, addressed to skilled readers, provides useful comments on the heat problem formulation. The Matlab procedure is proposed as a free code for educational purposes and can be extracted directly from the document using the standard copy and paste function.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer

Software:

top.m; Matlab
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References:

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