A small collection of closed-form solutions to PDE-based initial boundary value problems
With the product of trignonometric and exponential functions, closed-form solutions for the homogeneous heat equation, advection-diffusion equation, and homogeneous wave equation in 1D, 2D, and 3D are constructed. These are useful to benchmark numerical solvers like FEM.
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von Danwitz, M, Voulis, I, Hosters, N, Behr, M. Time-continuous and time-discontinuous space-time finite elements for advection-diffusion problems. Int J Numer Methods Eng. 2023; 1- 28. doi: 10.1002/nme.7241
Schuß, S, Glas, S, Hesch, C. Non-linear space-time elasticity. Int J Numer Methods Eng. 2023; 124( 9): 1965– 1990. doi: 10.1002/nme.7194