Mixed finite-element methods for Hamilton-Jacobi-Bellman-type equations

F. A. Milner; E. J. Park

doi:10.1093/imanum/16.3.399

Mixed finite-element methods for Hamilton-Jacobi-Bellman-type equations

F. A. Milner, E. J. Park

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

13 Scopus citations

Abstract

The numerical solution of Dirichlet's problem for a second-order elliptic operator in divergence form with arbitrary nonlinearities in the first-and zero-order terms is considered. The mixed finite-element method is used. Existence and uniqueness of the approximation are proved and optimal error estimates in L² are demonstrated for the relevant functions. Error estimates are also derived in L^q, 2 ≤ q ≤ + ∞.

Original language	English (US)
Pages (from-to)	399-412
Number of pages	14
Journal	IMA Journal of Numerical Analysis
Volume	16
Issue number	3
DOIs	https://doi.org/10.1093/imanum/16.3.399
State	Published - Jul 1996
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Computational Mathematics
Applied Mathematics

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10.1093/imanum/16.3.399

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title = "Mixed finite-element methods for Hamilton-Jacobi-Bellman-type equations",

abstract = "The numerical solution of Dirichlet's problem for a second-order elliptic operator in divergence form with arbitrary nonlinearities in the first-and zero-order terms is considered. The mixed finite-element method is used. Existence and uniqueness of the approximation are proved and optimal error estimates in L2 are demonstrated for the relevant functions. Error estimates are also derived in Lq, 2 ≤ q ≤ + ∞.",

author = "Milner, {F. A.} and Park, {E. J.}",

year = "1996",

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N2 - The numerical solution of Dirichlet's problem for a second-order elliptic operator in divergence form with arbitrary nonlinearities in the first-and zero-order terms is considered. The mixed finite-element method is used. Existence and uniqueness of the approximation are proved and optimal error estimates in L2 are demonstrated for the relevant functions. Error estimates are also derived in Lq, 2 ≤ q ≤ + ∞.

AB - The numerical solution of Dirichlet's problem for a second-order elliptic operator in divergence form with arbitrary nonlinearities in the first-and zero-order terms is considered. The mixed finite-element method is used. Existence and uniqueness of the approximation are proved and optimal error estimates in L2 are demonstrated for the relevant functions. Error estimates are also derived in Lq, 2 ≤ q ≤ + ∞.

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Mixed finite-element methods for Hamilton-Jacobi-Bellman-type equations

Abstract

ASJC Scopus subject areas

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