Standard finite elements for the numerical resolution of the elliptic Monge–Ampère equation: classical solutions
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چکیده
منابع مشابه
Standard Finite Elements for the Numerical Resolution of the Elliptic Monge-ampère Equation: Aleksandrov Solutions
We prove a convergence result for a natural discretization of the Dirichlet problem of the elliptic Monge-Ampère equation using finite dimensional spaces of piecewise polynomial C functions. Discretizations of the type considered in this paper have been previously analyzed in the case the equation has a smooth solution and numerous numerical evidence of convergence were given in the case of non...
متن کاملStandard Finite Elements for the Numerical Resolution of the Elliptic Monge-ampère Equation: Mixed Methods
We prove a convergence result for a mixed finite element method for the Monge-Ampère equation to its weak solution in the sense of Aleksandrov. The unknowns in the formulation are the scalar variable and the Hessian matrix.
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ژورنال
عنوان ژورنال: IMA Journal of Numerical Analysis
سال: 2014
ISSN: 0272-4979,1464-3642
DOI: 10.1093/imanum/dru028