[...] It is possible to skip this section and continue with the discretization stage and make use of the initialized data structures
ProcessEquationscreates. With this it is possible to use
ProcessEquationsas an equation preprocessor, for example, for a new numerical discretization method.
Currently, the only discretization method available in this framework is the finite element method. Thus, by default, InitializePDEMethodData generates a FEMMethodData object.
It is possible to implement a new spatial discretization method to plug in the
NDSolve framework? Does anyone tried/succeded in that? There is some reference/tutorial/skeleton implementation like the ones for time integration?
Second, related, question. Before the advent of Finite Element Framework in Mathematica 10, how Mathematica solved steady-state, boundary value problems? It is still possible to use the old method?
I know that, under
"PDEDiscretization" only supports
"MethodOfLines" we can apparently enable something like a finite difference discretization with
"SpatialDiscretization" -> "TensorProductGrid" but the whole
"MethodOfLines" it's unsuitable for steady state, elliptic problems.