Superconvergence and time evolution of discontinuous Galerkin finite element solutions

Journal of Computational Physics

Volumn 227, Issue 22, 2008, Pages 9612-9627

  Cheng, Yingda ^a   Shu, Chi Wang ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b BROWN UNIVERSITY   (United States)

Author keywords

Discontinuous Galerkin method; Error estimates; Projection; Superconvergence; Upwind flux

Indexed keywords

GALERKIN METHODS; NONLINEAR EQUATIONS; PIECEWISE LINEAR TECHNIQUES; POLYNOMIALS;

DISCONTINOUS GALERKIN METHODS; DISCONTINUOUS GALERKIN; ERROR ESTIMATES; EXACT SOLUTION; FINITE ELEMENT SOLUTION; GALERKIN FINITE ELEMENTS; PROJECTION; SUPER CONVERGENCE; TIME EVOLUTIONS; UPWIND FLUX;

ERRORS;

EID: 52749083843     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.07.010     Document Type: Article

References (13)

1. Adjerid S., Devine K., Flaherty J., and Krivodonova L. A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems. Computational Methods in Applied Mechanics and Engineering 191 (2002) 1097-1112
2. Adjerid S., and Massey T. Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem. Computational Methods in Applied Mechanics and Engineering 195 (2006) 3331-3346
3. Cockburn B., Hou S., and Shu C.-W. The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case. Mathematics of Computation 54 (1990) 545-581
4. Cockburn B., Lin S.-Y., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems. Journal of Computational Physics 84 (1989) 90-113
5. Cockburn B., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework. Mathematics of Computation 52 (1989) 411-435
6. Cockburn B., and Shu C.-W. The Runge-Kutta local projection P1-discontinuous Galerkin finite element method for scalar conservation laws. Mathematical Modelling and Numerical Analysis 25 (1991) 337-361
7. Cockburn B., and Shu C.-W. The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. Journal of Computational Physics 141 (1998) 199-224
8. Cockburn B., and Shu C.-W. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. Journal of Scientific Computing 16 (2001) 173-261
9. Cockburn B., and Shu C.-W. Foreword for the special issue on discontinuous Galerkin method. Journal of Scientific Computing 22-23 (2005) 1-3
10. Dawson C. Foreword for the special issue on discontinuous Galerkin method. Computer Methods in Applied Mechanics and Engineering 195 (2006) 3183
11. Gottlieb S., Shu C.-W., and Tadmor E. Strong stability preserving high order time discretization methods. SIAM Review 43 (2001) 89-112
12. Zhang M., and Shu C.-W. An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods. Computers and Fluids 34 (2005) 581-592
13. Zhang Q., and Shu C.-W. Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws. SIAM Journal on Numerical Analysis 42 (2004) 641-666