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High-order finite elements for efficient solution of transient heat diffusion problems with sharp thermal gradients

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conference contribution
posted on 13.05.2021, 13:18 by M. Iqbal, K Christodoulou, H. Gimperlein, M.S. Mohamed, O. Laghrouche
This work studies time stepping schemes for high-order finite elements applied to time-dependent heat diffusion problems with sharp gradients. As a test case p-version finite elements in space are used to capture the sharp thermal variations of the solution. Numerical results investigate the accuracy and limitations of backward Euler and Crank-Nicolson time stepping schemes for high polynomial orders in space. The results inform future work on high-order time discretizations for enriched finite element discretizations, which use non-polynomial basis functions to resolve nonsmooth features.

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