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A family of ELLAM schemes for advection-diffusion-reaction equations and their convergence analyses

✍ Scribed by Hong Wang

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 553 KB
Volume: 14
Category: Article
ISSN: 0749-159X
DOI: 10.1002/(sici)1098-2426(199811)14:6<739::aid-num3>3.0.co;2-r

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✦ Synopsis

A family of ELLAM (Eulerian-Lagrangian localized adjoint method) schemes is developed and analyzed for linear advection-diffusion-reaction transport partial differential equations with any combination of inflow and outflow Dirichlet, Neumann, or flux boundary conditions. The formulation uses space-time finite elements, with edges oriented along Lagrangian flow paths, in a time-stepping procedure, where space-time test functions are chosen to satisfy a local adjoint condition. This allows Eulerian-Lagrangian concepts to be applied in a systematic mass-conservative manner, yielding numerical schemes defined at each discrete time level. Optimal-order error estimates and superconvergence results are derived. Numerical experiments are performed to verify the theoretical estimates.

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