L²(H¹γ) finite element convergence for degenerate isotropic Hamilton–Jacobi–Bellman equations

Jensen, Max (2017) L²(H¹γ) finite element convergence for degenerate isotropic Hamilton–Jacobi–Bellman equations. IMA Journal of Numerical Analysis, 37 (3). pp. 1300-1316. ISSN 0272-4979

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Abstract

In this paper we study the convergence of monotone P1 finite element methods for fully nonlinear Hamilton–Jacobi–Bellman equations with degenerate, isotropic diffusions. The main result is strong convergence of the numerical solutions in a weighted Sobolev space L²(H¹γ(Ω)) to the viscosity solution without assuming uniform parabolicity of the HJB operator.

Item Type: Article
Keywords: Finite element methods, Degenerate partial differential equations, Hamilton–Jacobi–Bellman equations, Viscosity solutions
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Max Jensen
Date Deposited: 29 Sep 2016 14:10
Last Modified: 13 Jul 2017 10:26
URI: http://sro.sussex.ac.uk/id/eprint/63365

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