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arXiv · 1707.08459

High-order numerical methods for 2D parabolic problems in single and composite domains

Gustav Ludvigsson·Kyle R. Steffen·Simon Sticko·Siyang Wang·Qing Xia·Yekaterina Epshteyn·Gunilla Kreiss
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Abstract

In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at interfaces, considering (i) the Cut Finite Element Method; (ii) the Difference Potentials Method; and (iii) the summation-by-parts Finite Difference Method. First we give a brief introduction for each of the three methods. Next, we propose benchmark problems, and consider numerical tests-with respect to accuracy and convergence-for linear parabolic problems on a single domain, and continue with similar tests for linear parabolic problems on a composite domain (with the interface defined either explicitly or implicitly). Lastly, a comparative discussion of the methods and numerical results will be given.

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Gustav Ludvigsson, Kyle R. Steffen, Simon Sticko, Siyang Wang, Qing Xia, Yekaterina Epshteyn, Gunilla Kreiss. 2017-07-26. High-order numerical methods for 2D parabolic problems in single and composite domains. https://doi.org/10.1007/s10915-017-0637-y

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