منابع مشابه
Error estimate for finite volume scheme
The Finite Volume method is well adapted to the computation of the solution of pdes which are conservation (or balance) laws, for the reason that it respects the property of conservation of the pde under study. The mathematical analysis of the application of the Finite Volume method to hyperbolic first-order conservation laws can be dated from the mid sixties (see [TS62] for example). Concernin...
متن کاملSe p 20 05 Error estimate for the Finite Volume Scheme applied to the advection equation
We study the convergence of the Finite Volume Scheme for the advection equation with a divergence free C1 speed in a domain without boundary. We show that the rate of the L∞(0, T ;L1)-error estimate is h1/2 for BV data. This result was expected from numerical experiment and is optimal. The proof is based on Kuznetsov’s method. This method has been introduced for non-linear hyperbolic equations ...
متن کاملFinite volume schemes for nonhomogeneous scalar conservation laws: error estimate
In this paper, we study nite volume schemes for the nonhomogeneous scalar conservation law u t +divF(x; t; u) = q(x; t; u) with initial condition u(x; 0) = u 0 (x). The source term may be either stii or nonstii. In both cases, we prove error estimates between the approximate solution given by a nite volume scheme (the scheme is totally explicit in the nonstii case, semi-implicit in the stii cas...
متن کاملExplicit error bounds for an adaptive finite volume scheme
A new technique for the implementation of cell-centered finite volume schemes is proposed. It is based on an equivalence between these schemes and the non-conforming Crouzeix-Raviart finite element approximation. Though the implementation somewhat increases the number of unknowns, it brings two significant advantages that make it attractive. On the one hand the resulting formulation is well-def...
متن کاملJu n 20 06 Error estimate for the Finite Volume scheme applied to the linear advection equation
The Finite Volume method is well adapted to the computation of the solution of pdes which are conservation (or balance) laws, for the reason that it respects the property of conservation of the pde under study. The mathematical analysis of the application of the Finite Volume method to hyperbolic first-order conservation laws can be dated from the mid sixties (see [TS62] for example). Concernin...
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ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 2006
ISSN: 0029-599X,0945-3245
DOI: 10.1007/s00211-006-0053-y