A spectrum enveloping technique for convection-diffusion computations
Valipuram S. Manoranjan, R. DRAKE · IMA Journal of Numerical Analysis · 1993
In a convection-diffusion equation, if the convection term is very dominant, the linear system of equations which result from either finite-differencing or finite elementing will not have a strictly diagonally dominant coefficient matrix. So, if one tries a standard iteration method (Jacobi or Gauss-Seidel) to solve the linear system of equations, the iteration matrix may not satisfy the spectral radius condition for convergence and hence no converging solution may be obtained. The problem can be overcome, under certain conditions, if one uses the two step iteration/spectrum enveloping procedure of de Pillis in the format of a Jacobi method. This paper extends the two step iteration/spectrum enveloping idea to a Gauss-Seidel format for a model convection-diffusion problem.