A finite element method for fully nonlinear elliptic problems
Numerical Analysis
2015-03-19 v5
Abstract
We present a continuous finite element method for some examples of fully nonlinear elliptic equation. A key tool is the discretisation proposed in Lakkis & Pryer (2011, SISC) allowing us to work directly on the strong form of a linear PDE. An added benefit to making use of this discretisation method is that a recovered (finite element) Hessian is a biproduct of the solution process. We build on the linear basis and ultimately construct two different methodologies for the solution of second order fully nonlinear PDEs. Benchmark numerical results illustrate the convergence properties of the scheme for some test problems including the Monge-Amp\`ere equation and Pucci's equation.
Cite
@article{arxiv.1103.2970,
title = {A finite element method for fully nonlinear elliptic problems},
author = {Omar Lakkis and Tristan Pryer},
journal= {arXiv preprint arXiv:1103.2970},
year = {2015}
}
Comments
22 pages, 31 figures