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A family of ELLAM schemes for advection‐diffusion‐reaction equations and their convergence analyses
Author(s) -
Wang Hong
Publication year - 1998
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199811)14:6<739::aid-num3>3.0.co;2-r
Subject(s) - mathematics , advection , superconvergence , partial differential equation , inflow , eulerian path , flow (mathematics) , boundary value problem , convergence (economics) , mathematical analysis , finite element method , lagrangian , geometry , mechanics , physics , economics , thermodynamics , economic growth
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. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 739–780, 1998