A finite element method for fully nonlinear elliptic problems

Omar Lakkis; Tristan Pryer

doi:10.1137/120887655

A finite element method for fully nonlinear elliptic problems

Omar Lakkis
, Tristan Pryer

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

59 Citations (SciVal)

185 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 language	English
Pages (from-to)	A2025-A2045
Number of pages	21
Journal	SIAM Journal on Scientific Computing
Volume	35
Issue number	4
Early online date	6 Aug 2013
DOIs	https://doi.org/10.1137/120887655
Publication status	Published - 2013

Bibliographical note

22 pages, 31 figures

Keywords

math.NA
65N30, 65Y20, 35J60,

Access to Document

10.1137/120887655

1103.2970v5.PDF
(C) 2013, Society for Industrial and Applied Mathematics
Accepted author manuscript, 2.34 MBLicence: CC BY-NC

Cite this

@article{1675b67179574f368e4453e8b5a5e5df,

title = "A finite element method for fully nonlinear elliptic problems",

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\textbackslash{}`ere equation and Pucci's equation.",

keywords = "math.NA, 65N30, 65Y20, 35J60,",

author = "Omar Lakkis and Tristan Pryer",

note = "22 pages, 31 figures",

year = "2013",

doi = "10.1137/120887655",

language = "English",

volume = "35",

pages = "A2025--A2045",

journal = "SIAM Journal on Scientific Computing",

issn = "1064-8275",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "4",

}

TY - JOUR

T1 - A finite element method for fully nonlinear elliptic problems

AU - Lakkis, Omar

AU - Pryer, Tristan

N1 - 22 pages, 31 figures

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - math.NA

KW - 65N30, 65Y20, 35J60,

U2 - 10.1137/120887655

DO - 10.1137/120887655

M3 - Article

SN - 1064-8275

VL - 35

SP - A2025-A2045

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 4

ER -

A finite element method for fully nonlinear elliptic problems

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this