Incremental unknowns for convection-diffusion equations
The authors employ the method of incremental unknowns as suggested by the second author [SIAM J. Math. Anal. 21, No. 1, 154-178 (1990; Zbl 0715.35039)] to improve the convergence rate for some iterative methods applied to finite difference schemes for convection-diffusion equations. It is shown theoretically that, by use of incremental unknowns, condition numbers \((\nu(A)=\lambda_{\max}(A^ t A)^{1/2})/\lambda_{\min}(A+A^ t)\) with \(A+A^ t\) positive) are improved from \(O(h^{-2})\) to \(O((\log h)^ 2)\), when the mesh size \(h\to 0\). Convergence rates are also estimated -- by theoretical methods as well as by numerical tests.
scientific article; zbMATH DE number 166548