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L ∞ ‐error estimates of discontinuous Galerkin methods with theta time discretization scheme for an evolutionary HJB equations
Author(s) -
Boulaaras Salah,
Haiour Mohamed,
Bencheick Le hocine Med Amine
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4306
Subject(s) - mathematics , discretization , hamilton–jacobi–bellman equation , convergence (economics) , finite element method , dirichlet problem , dirichlet boundary condition , norm (philosophy) , scheme (mathematics) , dirichlet distribution , mathematical analysis , hamilton–jacobi equation , boundary value problem , mathematical optimization , bellman equation , physics , political science , law , economics , thermodynamics , economic growth
The main purpose of this paper is to analyze the convergence and regularity of our proposed algorithm of the finite element methods coupled with a theta time discretization scheme for evolutionary Hamilton‐Jacobi‐Bellman equations with linear source terms with respect to the Dirichlet boundary conditions (Appl. Math. Comput., 262 (2015), 42.55 ). Also, an optimal error estimate with an asymptotic behavior in uniform norm is given. Copyright © 2017 John Wiley & Sons, Ltd.