Jaroszkowski-Jensen2022_Article_FiniteElementMethodsForIsotrop.pdf (609.4 kB)
Finite element methods for isotropic Isaacs equations with viscosity and strong Dirichlet boundary conditions
Version 2 2023-06-12, 09:45
Version 1 2023-06-09, 23:11
journal contribution
posted on 2023-06-12, 09:45 authored by Bartosz Jaroszkowski, Max JensenWe 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.
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- Published
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Applied Mathematics and OptimizationISSN
1432-0606Publisher
SpringerExternal DOI
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85Page range
1-32Article number
a8Department affiliated with
- Mathematics Publications
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- Numerical Analysis and Scientific Computing Research Group Publications
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- Yes
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- Yes
Legacy Posted Date
2022-02-03First Open Access (FOA) Date
2022-05-16First Compliant Deposit (FCD) Date
2022-02-02Usage metrics
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