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A finite element method for nonlinear elliptic problems

Lakkis, O. and Pryer, T. (2013) A finite element method for nonlinear elliptic problems. SIAM Journal on Scientific Computing, 35 (4). A2025-A2045. ISSN 1095-7197

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To link to this item DOI: 10.1137/120887655

Abstract/Summary

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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:33811
Publisher:Society for Industrial and Applied Mathematics

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