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Journal of Scientific Computing

Erschienen in:

01.01.2013

Quadratic Finite Element Approximations of the Monge-Ampère Equation

verfasst von: Michael Neilan

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2013

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Abstract

We prove several new results of the C ⁰ finite element method introduced in (S.C. Brenner et al., Math. Comput. 80:1979–1995, 2011) for the fully nonlinear Monge-Ampère equation. These include the convergence of quadratic finite element approximations, W ^2,p quasi-optimal error estimates, localized pointwise error estimates, and convergence of Newton’s method with explicit dependence on the discretization parameter. Numerical experiments are presented which back up the theoretical results.

Vorheriger Artikel Analysis of an Interior Penalty Method for Fourth Order Problems on Polygonal Domains

Nächster Artikel On the Connection Between the Correction and Weighting Functions in the Correction Procedure via Reconstruction Method

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Titel: Quadratic Finite Element Approximations of the Monge-Ampère Equation
verfasst von: Michael Neilan
Publikationsdatum: 01.01.2013
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2013
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-012-9617-4

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