Recovery Based Linear Finite Element Methods for Hamilton–Jacobi–Bellman Equation with Cordes Coefficients

Abstract

SIAM Journal on Numerical Analysis, Volume 63, Issue 1, Page 23-53, February 2025.
Abstract. In this paper, we design a simple and convergent [math] linear finite element method for the linear second-order elliptic equation in nondivergence form and extend it to the Hamilton–Jacobi–Bellman equation. Motivated by the Miranda–Talenti estimate, we establish a discrete analogue of the estimate for the [math] linear finite element space based on a new gradient recovery operator. The construction and properties of the gradient recovery operator, including its superconvergent property on mildly structured meshes, are discussed. We provide a proof of convergence for the proposed methods and support the theory with numerical experiments.