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

Mathematics of Computation

Volumn 71, Issue 239, 2002, Pages 1075-1103

  Estep, Donald J ^a   Stuart, Andrew M ^a  

^a Veterinary Dentistry and Oral Surgery   (United States)

Author keywords

Attractors; Contractivity; Discontinuous Galerkin method; Dissipativity; Dynamical system; Existence; Initial value problems; Quadrature

Indexed keywords

EID: 0036018018     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-01-01364-3     Document Type: Article

References (17)

1. Discontinuous galerkin methods: Theory, computation and applications
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3. Discontinuous Galerkin methods for ordinary differential equations
4. A posteriori error bounds and global error control for approximations of ordinary differential equations
5. Estimating the error of numerical solutions of systems of nonlinear reaction-diffusion equations
6. The discontinuous Galerkin method for semilinear parabolic problems
7. Global dynamics of a discontinuous Galerkin approximation to a class of reaction-diffusion equations
8. Dissipativity of Runge-Kutta methods in Hilbert spaces
9. Global dissipativity for A-stable methods
10. Runge-kutta methods for dissipative and gradient dynamical systems
11. Error estimates and adaptive time step control for a class of one step methods for stiff ordinary differential equations