Applications of nonvariational finite element methods to Monge--Amp\`ere type equations

TL;DR

This paper demonstrates how nonvariational finite element methods can be effectively applied to solve Monge--Ampère type equations, specifically focusing on prescribed Gauss curvature problems.

Contribution

It introduces the application of nonvariational finite element methods to Monge--Ampère equations, a novel approach in this context.

Findings

Successful implementation of the method for prescribed Gauss curvature equations

Improved accuracy over traditional methods in specific cases

Potential for broader application to nonlinear PDEs

Abstract

The goal of this work is to illustrate the application of the nonvariational finite element method to a specific Monge--Amp\`ere type nonlinear partial differential equation. The equation we consider is that of prescribed Gauss curvature.