Adaptive C0 interior penalty methods for Hamilton–Jacobi–Bellman equations with Cordes coefficients
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TLDR
These estimates show the quasi-optimality of the method, and provide one with an adaptive finite element method that only assumes that the solution of the Hamilton-Jacobi-Bellman equation belongs to $H^2$.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2021-05-01 and is currently open access. It has received 17 citations till now. The article focuses on the topics: Penalty method & Partial differential equation.read more
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Journal ArticleDOI
Unified analysis of discontinuous Galerkin and $C^0$-interior penalty finite element methods for Hamilton--Jacobi--Bellman and Isaacs equations
Ellya L. Kawecki,Iain Smears +1 more
TL;DR: An abstract framework for the a priori error analysis of a broad family of numerical methods is introduced and the quasi-optimality of discrete approximations under three key conditions of Lipschitz continuity, discrete consistency and strong monotonicity of the numerical method is proved.
Journal ArticleDOI
Unified analysis of discontinuous Galerkin and C0-interior penalty finite element methods for Hamilton-Jacobi-Bellman and Isaacs equations
Ellya L. Kawecki,Iain Smears +1 more
TL;DR: In this paper, the authors provide a unified analysis of a posteriori and a priori error bounds for a broad class of discontinuous Galerkin and C 0 -IP finite element approximations of fully nonlinear second-order elliptic Hamilton-Jacobi-Bellman and Isaacs equations with Cordes coefficients.
Posted Content
Convergence of adaptive discontinuous Galerkin and $C^0$-interior penalty finite element methods for Hamilton--Jacobi--Bellman and Isaacs equations
Ellya L. Kawecki,Iain Smears +1 more
TL;DR: In this article, the authors prove the convergence of adaptive discontinuous Galerkin and interior penalty methods for fully nonlinear second-order elliptic Hamilton-Jacobi-Bellman and Isaacs equations with Cordes coefficients.
Journal ArticleDOI
Convergence of Adaptive Discontinuous Galerkin and $$C^0$$-Interior Penalty Finite Element Methods for Hamilton–Jacobi–Bellman and Isaacs Equations
Ellya L. Kawecki,Iain Smears +1 more
TL;DR: The convergence of adaptive discontinuous Galerkin and $C^0$-interior penalty methods for fully nonlinear second-order elliptic Hamilton--Jacobi--Bellman and Isaacs equations with Cordes coefficients is proved.
Journal ArticleDOI
C 0 finite element approximations of linear elliptic equations in non-divergence form and Hamilton–Jacobi–Bellman equations with Cordes coefficients
TL;DR: In this article, a non-standard finite element approximation of the linear elliptic equations in non-divergence form and the Hamilton-Jacobi-Bellman (HJB) equations with Cordes coefficients is proposed.
References
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Book
Controlled Markov processes and viscosity solutions
Wendell H. Fleming,H. Mete Soner +1 more
TL;DR: In this paper, an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions is given, as well as a concise introduction to two-controller, zero-sum differential games.
The FEniCS Project Version 1.5
Martin Sandve Alnæs,Jan Blechta,Johan Hake,August Johansson,Benjamin Kehlet,Anders Logg,Chris N. Richardson,Johannes Ring,Marie E. Rognes,Garth N. Wells +9 more
TL;DR: The FEniCS Project is a collaborative project for the development of innovative concepts and tools for automated scientific computing, with a particular focus on the solution of differential equations by finite element methods.
Journal ArticleDOI
A convergent adaptive algorithm for Poisson's equation
TL;DR: In this paper, a converging adaptive algorithm for linear elements applied to Poisson's equation in two space dimensions is presented, and it is proved that the error, measured in the energy norm, decreases at a constant rate in each step until a prescribed error bound is reached.
Journal ArticleDOI
Poincaré-Friedrichs Inequalities for Piecewise H 1 Functions
TL;DR: Poincare--Friedrichs inequalities for piecewise H1 functions are established and can be applied to classical nonconforming finite element methods, mortar methods, and discontinuous Galerkin methods.
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