Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method
نویسندگان
چکیده
In this paper we derive a priori and a posteriori error estimates for cell centered finite volume approximations of nonlinear conservation laws on polygonal bounded domains. Numerical experiments show the applicability of the a posteriori result for the derivation of local adaptive solution strategies.
منابع مشابه
A new total variation diminishing implicit nonstandard finite difference scheme for conservation laws
In this paper, a new implicit nonstandard finite difference scheme for conservation laws, which preserving the property of TVD (total variation diminishing) of the solution, is proposed. This scheme is derived by using nonlocal approximation for nonlinear terms of partial differential equation. Schemes preserving the essential physical property of TVD are of great importance in practice. Such s...
متن کاملRelative Entropy for the Finite Volume Approximation of Strong Solutions to Systems of Conservation Laws
We study in this paper the finite volume approximation of strong solutions to systems of conservation laws. We derive error estimates in the multidimensional case, using the relative entropy between the strong solution and its finite volume approximation. The error terms are carefully studied, leading to a classical h1/2 estimate under a BV assumption on the numerical approximation.
متن کاملAn Error Estimate for Finite Volume Methods for Multidimensional Conservation Laws
In this paper, an L°°(Ll )-error estimate for a class of finite volume methods for the approximation of scalar multidimensional conservation laws is obtained. These methods can be formally high-order accurate and are defined on general triangulations. The error is proven to be of order ft'/4 , where h represents the "size" of the mesh, via an extension of Kuznetsov approximation theory for whic...
متن کاملA posteriori error estimation for the Lax-Wendroff finite difference scheme
In many application domains, the preferred approaches to the numerical solution of hyperbolic partial differential equations such as conservation laws are formulated as finite difference schemes. While finite difference schemes are amenable to physical interpretation, one disadvantage of finite difference formulations is that it is relatively difficult to derive the so-called goal oriented a po...
متن کاملNumerical approximation of stochastic conservation laws on bounded domains
This paper is devoted to the study of finite volume methods for the discretization of scalar conservation laws with a multiplicative stochastic force defined on a bounded domain D of R with Dirichlet boundary conditions and a given initial data in L(D). We introduce a notion of stochastic entropy process solution which generalizes the concept of weak entropy solution introduced by F.Otto for su...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Math. Comput.
دوره 75 شماره
صفحات -
تاریخ انتشار 2006