TY - JOUR
T1 - Error estimates for finite element methods for scalar conservation laws
AU - Cockburn, Bernardo
AU - Gremaud, Pierre Alain
PY - 1996/4
Y1 - 1996/4
N2 - In this paper, new a posteriori error estimates for the shock-capturing streamline diffusion (SCSD) method and the shock-capturing discontinuous galerkin (SCDG) method for scalar conservation laws are obtained. These estimates are then used to prove that the SCSD method and the SCDG method converge to the entropy solution with a rate of at least h1/8 and h1/4, respectively, in the L∞(L1)-norm. The triangulations are made of general acute simplices and the approximate solution is taken to be piecewise a polynomial of degree k. The result is independent of the dimension of the space.
AB - In this paper, new a posteriori error estimates for the shock-capturing streamline diffusion (SCSD) method and the shock-capturing discontinuous galerkin (SCDG) method for scalar conservation laws are obtained. These estimates are then used to prove that the SCSD method and the SCDG method converge to the entropy solution with a rate of at least h1/8 and h1/4, respectively, in the L∞(L1)-norm. The triangulations are made of general acute simplices and the approximate solution is taken to be piecewise a polynomial of degree k. The result is independent of the dimension of the space.
KW - Discontinuous galerkin method
KW - Error estimates
KW - Multidimensional conservation laws
KW - Streamline diffusion method
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U2 - 10.1137/0733028
DO - 10.1137/0733028
M3 - Article
AN - SCOPUS:0002154319
SN - 0036-1429
VL - 33
SP - 522
EP - 554
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
IS - 2
ER -