A meshfree method for solving the Monge-Ampere equation

被引：10

作者：

Boehmer, Klaus ^{[1
]}

Schaback, Robert ^{[2
]}

机构：

[1] Univ Marburg, Fachbereich Math & Informat, Arbeitsgrp Numer, Hans Meerwein Str, D-35032 Marburg, Germany

[2] Univ Gottingen, Inst Numer & Angew Math, Lotzestr 16-18, D-37073 Gottingen, Germany

来源：

NUMERICAL ALGORITHMS | 2019年 / 82卷 / 02期

关键词：

Collocation; Fully nonlinear PDE; Monge-Ampere; Nonlinear optimizer; MATLAB implementation; Convergence; Error analysis; Error estimates; SCHEMES;

D O I：

10.1007/s11075-018-0612-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper solves the two-dimensional Dirichlet problem for the Monge-Ampere equation by a strong meshless collocation technique that uses a polynomial trial space and collocation in the domain and on the boundary. Convergence rates may be up to exponential, depending on the smoothness of the true solution, and this is demonstrated numerically and proven theoretically, applying a sufficiently fine collocation discretization. A much more thorough investigation of meshless methods for fully nonlinear problems is in preparation.

引用

页码：539 / 551

页数：13

共 24 条

[1]

[Anonymous], 2007, SMOOTH FINITE ELEMEN

[2]

[Anonymous], NONLINEAR DISCRETIZA

[3]

[Anonymous], 2015, INTERDISCIPLINARY MA

[4] On Standard Finite Difference Discretizations of the Elliptic Monge-AmpSre Equation [J].

Awanou, Gerard .

JOURNAL OF SCIENTIFIC COMPUTING, 2016, 69 (02) :892-904

[5] Spline element method for Monge-Ampere equations [J].

Awanou, Gerard .

BIT NUMERICAL MATHEMATICS, 2015, 55 (03) :625-646

[6] TWO NUMERICAL METHODS FOR THE ELLIPTIC MONGE-AMPERE EQUATION [J].

Benamou, Jean-David ;

Froese, Brittany D. ;

Oberman, Adam M. .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2010, 44 (04) :737-758

[7] A nonlinear discretization theory [J].

Boehmer, Klaus ;

Schaback, Robert .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 254 :204-219

[8] On finite element methods for fully nonlinear elliptic equations of second order [J].

Boehmer, Klaus .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2008, 46 (03) :1212-1249

[9]

Bohmer K., 2010, Numerical methods for nonlinear elliptic differential equations

[10]

Braess D., 2001, Finite Elements, in Theory, Fast Solvers, and Applications in Solid Mechanics, VSecond

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