The dynamical behavior of the discontinuous Galerkin method and related difference schemes

DOI10.1090/S0025-5718-01-01364-3zbMath0998.65080MaRDI QIDQ4529708

Donald J. Estep, Andrew M. Stuart

Publication date: 6 May 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

stabilitynumerical examplesdissipativityinitial value problemsquadratureRunge-Kutta schemesdiscontinuous Galerkin finite element method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Finite difference and finite volume methods for ordinary differential equations (65L12)

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Discrete conservation laws for finite element discretisations of multisymplectic PDEs ⋮ Global dynamics of a discontinuous Galerkin approximation to a class of reaction-diffusion equation ⋮ Efficient goal-oriented global error estimators for BDF methods using discrete adjoints ⋮ Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes ⋮ Discontinuous Galerkin and related methods for ODE ⋮ On the development of symmetry-preserving finite element schemes for ordinary differential equations ⋮ A posteriori error analysis for finite element methods with projection operators as applied to explicit time integration techniques ⋮ A posteriori error analysis for higher order dissipative methods for evolution problems ⋮ A unified discontinuous Galerkin framework for time integration ⋮ Global error control for the continuous Galerkin finite element method for ordinary differential equations ⋮ Variational time discretizations of higher order and higher regularity ⋮ Unified analysis for variational time discretizations of higher order and higher regularity applied to non-stiff ODEs

Cites Work

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• Dissipativity of Runge-Kutta methods in Hilbert spaces
• Infinite-dimensional dynamical systems in mechanics and physics
• Global dynamics of a discontinuous Galerkin approximation to a class of reaction-diffusion equation
• Global Dissipativity for A-Stable Methods
• Discontinuous Polynomial Approximations in the Theory of One-Step, Hybrid and Multistep Methods for Nonlinear Ordinary Differential Equations
• Error Estimates and Adaptive Time-Step Control for a Class of One-Step Methods for Stiff Ordinary Differential Equations
• Discontinuous Galerkin Methods for Ordinary Differential Equations
• The discontinuous Galerkin method for semilinear parabolic problems
• Runge–Kutta Methods for Dissipative and Gradient Dynamical Systems
• A Posteriori Error Bounds and Global Error Control for Approximation of Ordinary Differential Equations
• Estimating the error of numerical solutions of systems of reaction-diffusion equations