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arXiv · 1507.00140

$L^2(H^1_γ)$ Finite Element Convergence for Degenerate Isotropic Hamilton-Jacobi-Bellman Equations

Max Jensen
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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 $L^2(H^1_γ(Ω))$ to the viscosity solution without assuming uniform parabolicity of the HJB operator.

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Max Jensen. 2015-07-01. $L^2(H^1_γ)$ Finite Element Convergence for Degenerate Isotropic Hamilton-Jacobi-Bellman Equations. https://arxiv.org/abs/1507.00140

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