Mixed Finite Element Approximation of the Hamilton--Jacobi--Bellman Equation with Cordes Coefficients

Dietmar  Gallistl; Endre Süli

doi:10.1137/18M1192299

Mixed Finite Element Approximation of the Hamilton--Jacobi--Bellman Equation with Cordes Coefficients

Dietmar Gallistl, Endre Süli

Mathematics of Computational Science

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Abstract

A mixed finite element approximation of $H^2$ solutions to the fully nonlinear Hamilton--Jacobi--Bellman equation, with coefficients that satisfy the Cordes condition, is proposed and analyzed. A priori and a posteriori bounds on the approximation error are proved. The contributions from the a posteriori error estimator can be used as refinement indicators in an adaptive mesh-refinement algorithm. The convergence of this procedure is proved and empirically studied in numerical experiments

Original language	English
Pages (from-to)	592-614
Number of pages	23
Journal	SIAM journal on numerical analysis
Volume	57
Issue number	2
DOIs	https://doi.org/10.1137/18M1192299
Publication status	Published - 19 Mar 2019

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title = "Mixed Finite Element Approximation of the Hamilton--Jacobi--Bellman Equation with Cordes Coefficients",

abstract = "A mixed finite element approximation of $H^2$ solutions to the fully nonlinear Hamilton--Jacobi--Bellman equation, with coefficients that satisfy the Cordes condition, is proposed and analyzed. A priori and a posteriori bounds on the approximation error are proved. The contributions from the a posteriori error estimator can be used as refinement indicators in an adaptive mesh-refinement algorithm. The convergence of this procedure is proved and empirically studied in numerical experiments",

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AU - Gallistl, Dietmar

AU - Süli, Endre

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Y1 - 2019/3/19

N2 - A mixed finite element approximation of $H^2$ solutions to the fully nonlinear Hamilton--Jacobi--Bellman equation, with coefficients that satisfy the Cordes condition, is proposed and analyzed. A priori and a posteriori bounds on the approximation error are proved. The contributions from the a posteriori error estimator can be used as refinement indicators in an adaptive mesh-refinement algorithm. The convergence of this procedure is proved and empirically studied in numerical experiments

AB - A mixed finite element approximation of $H^2$ solutions to the fully nonlinear Hamilton--Jacobi--Bellman equation, with coefficients that satisfy the Cordes condition, is proposed and analyzed. A priori and a posteriori bounds on the approximation error are proved. The contributions from the a posteriori error estimator can be used as refinement indicators in an adaptive mesh-refinement algorithm. The convergence of this procedure is proved and empirically studied in numerical experiments

U2 - 10.1137/18M1192299

DO - 10.1137/18M1192299

M3 - Article

VL - 57

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EP - 614

JO - SIAM journal on numerical analysis

JF - SIAM journal on numerical analysis

SN - 0036-1429

IS - 2

ER -

Mixed Finite Element Approximation of the Hamilton--Jacobi--Bellman Equation with Cordes Coefficients

Abstract

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