Superconvergence and time evolution of discontinuous Galerkin finite element solutions

Authors:
Yingda Cheng;Chi-Wang Shu
Affiliations:
Department of Mathematics and ICES, University of Texas, Austin, TX 78712, USA;Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Venue:
Journal of Computational Physics
Year:
2008

Citing 6
Cited 6

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Abstract

In this paper, we study the convergence and time evolution of the error between the discontinuous Galerkin (DG) finite element solution and the exact solution for conservation laws when upwind fluxes are used. We prove that if we apply piecewise linear polynomials to a linear scalar equation, the DG solution will be superconvergent towards a particular projection of the exact solution. Thus, the error of the DG scheme will not grow for fine grids over a long time period. We give numerical examples of P^k polynomials, with 1=