On the Solution of Convection-diffusion Boundary Value Problems by Grid Adaptation

The eeect of grid adaptation on the numerical solution of model convection-diiusion equations with a conservation form is studied. The grid adaptation technique studied is based on an equi-distribution principle. In particular a parameter dependent monitor function is introduced which incorporates xed meshes, approximate arc-legth equi-distribution and equi-distribution of the absolute value of the solution, in a single framework. Thus the resulting numerical method is a coupled nonlinear system of equations for the mesh spacings and the nodal values. A class of singularly perturbed problems, including Burger's equation in the limit of small viscosity, is studied. Singular perturbation and bifurcation techniques are used to analyse the solution of the discretized equations and numerical results are compared with the results from the analysis. Computation of the bifurcation diagram of the system is performed numerically using a continuation method and the results are used to illustrate the theory.