Minimum residual discretization of a semilinear elliptic problem
Numerical Analysis
2026-04-01 v1 Numerical Analysis
Abstract
We propose a least-squares penalization as a means to extend the discontinuous Petrov-Galerkin (DPG) method with optimal test functions to a class of semilinear elliptic problems. The nonlinear contributions are replaced with independent unknowns so that standard DPG techniques apply to the then linear problem with non-trivial kernel. The nonlinear relations are added as least-squares constraints. Assuming solvability of the semilinear problem and an Aubin-Nitsche-type approximation property for the primal variable, we prove a Cea estimate for the approximation error in canonical norms. Numerical results with uniform and adaptively refined meshes illustrate the performance of the scheme.
Cite
@article{arxiv.2603.29863,
title = {Minimum residual discretization of a semilinear elliptic problem},
author = {Carlos García Vera and Norbert Heuer and Dirk Praetorius},
journal= {arXiv preprint arXiv:2603.29863},
year = {2026}
}