β Scribed by Do Y. Kwak
No coin nor oath required. For personal study only.
We give a norm estimate for the alternating direction implicit method for nonsymmetric elliptic convection-diffusion problems on a rectangular domain. We estimate a certain form of the iteration matrix in terms of the coefficients of convective terms and the mesh size. The norm is shown to be.asymptotically of the form (1 -Ch)/(l + Ch), where C is the same constant as in the symmetric case. We also show that the optimal size of the parameter is the same as in the symmetric case.
As a consequence, we conclude that the convergence behavior is as good as that of the symmetric case and does not deteriorate as the size of convective terms grows. Numerical experiment shows that our analysis is sharp.
π SIMILAR VOLUMES
## Abstract We propose, analyze, and implement fully discrete twoβtime level CrankβNicolson methods __with quadrature__ for solving secondβorder hyperbolic initial boundary value problems. Our algorithms include a practical version of the ADI scheme of Fernandes and Fairweather [SIAM J Numer Anal 2
This paper presents a row relaxation method for solving the regularized C, , least norm problem where e and p are positive constants, 1 < p < 03. The interest that we have in this problem lies in the observation that for small values of E the minimizer of P ( X ) is a good substitute for a minimizer
In this paper we present a residual-based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous Galerkin approximations of elliptic problems. The theory is developed for an elliptic model problem in two and three spatial dimensions and general