Dawson, Clint N.2018-06-182018-06-181994-06Dawson, Clint N.. "High Resolution Upwind-Mixed Finite Element Methods for Advection-Diffusion Equations with Variable Time-Stepping." (1994) <a href="https://hdl.handle.net/1911/101838">https://hdl.handle.net/1911/101838</a>.https://hdl.handle.net/1911/101838Numerical methods for advection-diffusion equations are discussed based on approximating advection using a high-resolution upwind finite difference method, and incorporating diffusion using a mixed finite element method. In this approach, advection is approximated explicitly and diffusion implicitly. We first describe the basic procedure where each advection time-step is followed by a diffusion step. Because the explicit nature of the advective scheme requires a CFL time-step constraint, the basic procedure may be expensive, especially if the CFL constraint is severe. Two alternative time-stepping approaches are presented for improving computational efficiency while preserving accuracy. In the first approach, several advective time-steps are computed before taking a diffusion step. In the second approach, the advective time steps are also allowed to vary spatially. Numerical results for these three procedures for a model problem arising in flow through porous media are given.20 ppengTechnical reportTR94-23