Unified analysis of discontinuous Galerkin andC0-interior penalty finite element methods for Hamilton–Jacobi–Bellman and Isaacs equations

DOI10.1051/m2an/2020081zbMath1477.65225arXiv2006.07202OpenAlexW3107809490MaRDI QIDQ5006314

Iain Smears, Ellya L. Kawecki

Publication date: 13 August 2021

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.07202

zbMATH Keywords

error analysisfully nonlinear PDEnonconforming finite element methodscordes conditionHamilton-Jacobi-Bellman and Isaacs equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) KdV equations (Korteweg-de Vries equations) (35Q53) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30) Hamilton-Jacobi equations (35F21) Strong solutions to PDEs (35D35)

Related Items (12)

Nonstandard finite element methods. Abstracts from the workshop held January 10--16, 2021 (hybrid meeting) ⋮ Convergence of adaptive discontinuous Galerkin and \(C^0\)-interior penalty finite element methods for Hamilton-Jacobi-Bellman and Isaacs equations ⋮ Discontinuous Galerkin methods for a class of nonvariational problems ⋮ Discontinuous Galerkin and C⁰-IP finite element approximation of periodic Hamilton–Jacobi–Bellman–Isaacs problems with application to numerical homogenization ⋮ Auxiliary space preconditioners for a \(C^0\) finite element approximation of Hamilton-Jacobi-Bellman equations with cordes coefficients ⋮ Stochastic streamflow and dissolved silica dynamics with application to the worst-case long-run evaluation of water environment ⋮ Plain convergence of goal-oriented adaptive FEM ⋮ A \(C^0\) finite element approximation of planar oblique derivative problems in non-divergence form ⋮ Numerical methods for fully nonlinear and related PDEs. Abstracts from the workshop held June 27 -- July 3, 2021 (hybrid meeting) ⋮ A priori error estimates for finite element approximations of regularized level set flows in higher norms ⋮ Residual-Based A Posteriori Error Estimates for $hp$-Discontinuous Galerkin Discretizations of the Biharmonic Problem ⋮ Mixed Finite Element Approximation of Periodic Hamilton--Jacobi--Bellman Problems With Application to Numerical Homogenization

Uses Software

• NGSolve

Cites Work

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