Numerical solution of fully nonlinear elliptic equations by Böhmer’s method

Abstract

We present an implementation of Böhmer’s finite element method for fully nonlinear elliptic partial differential equations on convex polygonal domains, based on a modified Argyris element and Bernstein–Bézier techniques. Our numerical experiments for several test problems, involving the classical Monge–Ampère equation and an unconditionally elliptic equation, confirm the convergence and error bounds predicted by Böhmer’s theoretical results.