Finite element methods for isotropic Isaacs equations with viscosity and strong Dirichlet boundary conditions

Jaroszkowski, Bartosz and Jensen, Max (2022) Finite element methods for isotropic Isaacs equations with viscosity and strong Dirichlet boundary conditions. Applied Mathematics and Optimization, 85. a8 1-32. ISSN 1432-0606

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Abstract

We study monotone P1 finite element methods on unstructured meshes for fully non-linear, degenerately parabolic Isaacs equations with isotropic diffusions arising from stochastic game theory and optimal control and show uniform convergence to the viscosity solution. Elliptic projections are used to manage singular behaviour at the boundary and to treat a violation of the consistency conditions from the framework by Barles and Souganidis by the numerical operators. Boundary conditions may be imposed in the viscosity or in the strong sense, or in a combination thereof. The presented monotone numerical method has well-posed finite dimensional systems, which can be solved efficiently with Howard’s method.

Item Type: Article
Keywords: Finite element methods, Isaacs equations, Bellman equations, fully nonlinear, viscosity solution, boundary conditions
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Max Jensen
Date Deposited: 03 Feb 2022 10:08
Last Modified: 16 May 2022 14:45
URI: http://sro.sussex.ac.uk/id/eprint/97466

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