A weak Galerkin method and its two‐grid algorithm for the quasi‐linear elliptic problems of non‐monotone type

Abstract

AbstractIn this article, a weak Galerkin (WG) method is first presented and analyzed for the quasi‐linear elliptic problem of non‐monotone type. By using Brouwer's fixed point technique, the existence of WG solution and error estimates in both the energy norm and the norm are derived. Then an efficient two‐grid WG method is introduced to improve the computational efficiency. The convergence error of the two‐grid WG method is analyzed in the energy norm. Numerical experiments are presented to verify our theoretical findings.