Manufactured solutions for the heat equation
I have compiled a python module that is ready to be used to check numerical routines, in particular time integration schemes or linear solvers, by means of manufactored solutions.
It considers the heat equation, takes a sympy expression as analytical solution, provides the stiffness and mass matrix from FEniCS as scipy sparse matrices, and it comes with methods to retrieve the current (in time) source term, analytical solution, and the approximation error.
Feel free to check it out from mit github account. There is also a link to the documentation.https://github.com/highlando/manufacsols-4-heateqn