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A finite element method for nonlinear elliptic problems

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journal contribution
posted on 2023-06-08, 15:50 authored by Omar LakkisOmar Lakkis, Tristan Pryer
We present a Galerkin method with piecewise polynomial continuous elements for fully nonlinear elliptic equations. A key tool is the discretization proposed in Lakkis and Pryer, 2011, allowing us to work directly on the strong form of a linear PDE. An added benefit to making use of this discretization method is that a recovered (finite element) Hessian is a byproduct of the solution process. We build on the linear method 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 as well as the Monge--Amp`ere equation and the Pucci equation.

History

Publication status

  • Published

File Version

  • Published version

Journal

SIAM Journal on Scientific Computing

ISSN

1064-8275

Publisher

Society for Industrial and Applied Mathematics

Issue

4

Volume

35

Article number

A2025-A2045

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2013-09-19

First Open Access (FOA) Date

2013-09-19

First Compliant Deposit (FCD) Date

2013-09-18

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