A nonvariational finite element method for fully nonlinear elliptic problems

Details A nonvariational finite element method for fully nonlinear elliptic problems A nonvariational finite element method for fully nonlinear elliptic problems

2011-03-15

arxiv.org/abs/1103.2970v4

Mathematics

Numerical Analysis

15 pages, 6 figures

Scientific paper

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\emph{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 \MA equation and Pucci's equation.

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