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

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.