A least-squares Galerkin gradient recovery method for fully nonlinear elliptic equations

Abstract

We propose a least squares Galerkin based gradient recovery to approximate Dirichlet problems for strong solutions of linear elliptic problems in nondivergence form and corresponding apriori and aposteriori error bounds. This approach is used to tackle fully nonlinear elliptic problems, e.g., Monge-Amp\`ere, Hamilton-Jacobi-Bellman, using the smooth (vanilla) and the semismooth Newton linearization. We discuss numerical results, including adaptive methods based on the aposteriori error indicators.