The proximal Galerkin method for non-symmetric variational inequalities
Numerical Analysis
2026-02-17 v1 Numerical Analysis
Abstract
We introduce the proximal Galerkin (PG) method for non-symmetric variational inequalities. The proposed approach is asymptotically mesh-independent and yields constraint-preserving approximations. We present both a conforming PG formulation and a hybrid mixed first-order system variant (FOSPG). We establish optimal a priori error estimates for each variant, which are verified numerically. We conclude by applying the method to American option pricing, free boundary problems in porous media, advection-diffusion with a semipermeable boundary, and the enforcement of discrete maximum principles.
Keywords
Cite
@article{arxiv.2602.14967,
title = {The proximal Galerkin method for non-symmetric variational inequalities},
author = {Guosheng Fu and Brendan Keith and Dohyun Kim and Rami Masri and Will Pazner},
journal= {arXiv preprint arXiv:2602.14967},
year = {2026}
}