L-error Estimate for a Finite Volume Approximation of Linear Advection
نویسنده
چکیده
Abstract. We study the convergence of the upwind Finite Volume scheme applied to the linear advection equation with a Lipschitz divergence-free speed in Rd . We prove a h1/2−ε-error estimate in the L∞(Rd × [0, T ])-norm for Lipschitz initial data. The expected optimal result is a h1/2-error estimate. In a second part, we also prove a h1/2-error estimate in the L(0, T ; L2(Rd))-norm for initial data in H1(Rd).
منابع مشابه
A Method to Calculate Numerical Errors Using Adjoint Error Estimation for Linear Advection
Abstract. This paper is concerned with the computation of numerical discretization error for uncertainty quantification. An a posteriori error formula is described for a functional measurement of the solution to a scalar advection equation that is estimated by finite volume approximations. An exact error formula and computable error estimate are derived based on an abstractly defined approximat...
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 کاملAdaptive Basis Enrichment for the Reduced Basis Method Applied to Finite Volume Schemes
We derive an efficient reduced basis method for finite volume approximations of parameterized linear advection-diffusion equations. An important step in deriving a reduced finite volume model with the reduced basis technology is the generation of a reduced basis space, on which the detailed numerical simulations are projected. We present a new strategy for this reduced basis generation. We appl...
متن کاملOptimal order finite element approximation for a hyperbolic integro-differential equation
Semidiscrete finite element approximation of a hyperbolic type integro-differential equation is studied. The model problem is treated as the wave equation which is perturbed with a memory term. Stability estimates are obtained for a slightly more general problem. These, based on energy method, are used to prove optimal order a priori error estimates.
متن کاملApproximation of stochastic advection diffusion equations with finite difference scheme
In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...
متن کامل