A posteriori error estimation for the Lax–Wendroff finite difference scheme

A 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...

A Posteriori Error Estimator for a Front-Fixing Finite Difference Scheme for American Options

In this paper, we present an MATLAB version of a finite difference scheme for the numerical solution of the American option valuation problem. Our main contribute is the definition of a posteriori error estimator for the American options pricing which is based on Richardson’s extrapolation theory. This error estimator allows us to find a suitable grid where the computed solution, both the optio...

A Posteriori Finite Element Error Estimation for Diffusion Problems

Adjerid et al. 2] and Yu 19, 20] show that a posteriori estimates of spatial discretiza-tion errors of piecewise bi-p polynomial nite element solutions of elliptic and parabolic problems on meshes of square elements may be obtained from jumps in solution gradients at element vertices when p is odd and from local elliptic or parabolic problems when p is even. We show that these simple error esti...

Efficient A Posteriori Error Estimation for Finite Volume Methods

The propagation of error in numerical solutions of the compressible Navier-Stokes equations is examined using linearized, and adjoint linearized versions of the discrete flow solver. With the forward linearization it is possible, given a measure of the local residual error in the field, to obtain estimates of global solution error. This allows for example the computation of error estimates on p...

A posteriori error estimation for ellipti eigenproblems