Python FEM and Multiphysics Simulations with FEniCS and FEATool
FEniCS is a flexible and comprehensive finite element FEM and partial differential equation PDE modeling and simulation toolkit with Python and C++ interface...
can in FEATool simply be written as
u' - D*(ux_x + uy_y) = 1
The parser will process this equation string and decompose it into the constituents of the finite element weak formulation which is used by the assembly and solver routines. Moreover, other physics modes can similarly be changed to accommodate custom additions to the pre-defined equations.
An example showing how to implement a custom equation model, solving a Black-Scholes example equation for financial derivative modeling, can found in the Tutorial section of the FEATool Users Guide
FEATool Custom Equation Tutorial