Error estimates to smooth solutions of semi-discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws
- Tsinghua Univ., Beijing (China)
- Brown Univ., Providence, RI (United States)
In this article, we focus on error estimates to smooth solutions of semi‐discrete discontinuous Galerkin (DG) methods with quadrature rules for scalar conservation laws. The main techniques we use are energy estimate and Taylor expansion first introduced by Zhang and Shu in (Zhang and Shu, SIAM J Num Anal 42 (2004), 641–666). We show that, with (piecewise polynomials of degree k ) finite elements in 1D problems, if the quadrature over elements is exact for polynomials of degree , error estimates of are obtained for general monotone fluxes, and optimal estimates of are obtained for upwind fluxes. For multidimensional problems, if in addition quadrature over edges is exact for polynomials of degree , error estimates of are obtained for general monotone fluxes, and are obtained for monotone and sufficiently smooth numerical fluxes. Numerical results validate our analysis. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 467–488, 2017
- Research Organization:
- Brown Univ., Providence, RI (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC); National Science Foundation (NSF)
- Grant/Contract Number:
- FG02-08ER25863; DMS-1418750; DE‐FG02‐08ER25863
- OSTI ID:
- 1533199
- Alternate ID(s):
- OSTI ID: 1401007
- Journal Information:
- Numerical Methods for Partial Differential Equations, Vol. 33, Issue 2; ISSN 0749-159X
- Publisher:
- WileyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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