I am interested in adaptive mesh methods for numerical solution of PDEs with applications to finance. As part of a school project, I have been pricing vanilla European call and put options using 2D FEM (space+time) and successfully applied an adaptive mesh algorithm to reduce the numerical error introduced by non-smooth payoffs.
I have not been able to find a lot of existing work on 2D space-time FEM in finance, let alone adaptive mesh methods in this context. Hence the question: do people tend to use FDMs due to ease of implementation (separate discretisation of the dimensions is much easier to handle code-wise), or are there other reasons for the apparent absence of space-time FEM in the literature?
I am contemplating whether or not it makes sense to keep working in this direction, as the lack of similar papers/works in progress might suggest that it is not of any relevance. If I have missed any existing papers on this topic, please provide references if possible.