论文信息 - Error estimates for finite element methods for scalar conservation laws

Error estimates for finite element methods for scalar conservation laws

In this paper, new a posteriors 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 $h^{{1 / 8}} $ and $h^{{1 / 8}} $, respectively, in the $L^\infty (L^1 )$-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.

Bernardo Cockburn | P. Gremaud

[1] James M. Ortega,et al. Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[2] N. N. Kuznetsov. Accuracy of some approximate methods for computing the weak solutions of a first-order quasi-linear equation , 1976 .

[3] R. J. Diperna,et al. Measure-valued solutions to conservation laws , 1985 .

[4] Thomas J. R. Hughes,et al. A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems , 1986 .

[5] Peter Hansbo,et al. On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws , 1990 .

[6] R. D. Murphy,et al. Iterative solution of nonlinear equations , 1994 .