A finite element method for fully nonlinear elliptic problems

Omar Lakkis, Tristan Pryer

Research output: Contribution to journalArticle

23 Citations (Scopus)
18 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)A2025-A2045
Number of pages21
JournalSIAM Journal on Scientific Computing
Volume35
Issue number4
Early online date6 Aug 2013
DOIs
Publication statusPublished - 2013

Keywords

  • math.NA
  • 65N30, 65Y20, 35J60,

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