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An ELLAM scheme for advection-diffusion equations in two dimensions. (English) Zbl 0939.65109

An Eulerian-Lagrangian localized adjoint method (ELLAM) is developed to solve two-dimensional advection-diffusion equations with all combinations of inflow and outflow Dirichlet, Neumann and flux boundary conditions. The ELLAM method provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes.
The computational advantages of the ELLAM approximation are demonstrated for a number of one-dimensional transport systems. Practical implementations of those schemes in multiple spatial dimensions are discussed. Numerical results are presented to compare the ELLAM scheme with many widely used numerical methods and to demonstrate advantages of this scheme.

MSC:

65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
35L15 Initial value problems for second-order hyperbolic equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
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