Abstract
In this paper, we develop Eulerian-Lagrangian localized adjoint methods (ELLAM) to solve the initial-boundary value problems for linear advection or advection-reaction equations. In contrast to many methods for advection-type problems, our ELLAM scheme naturally incorporates the inflow boundary conditions into its formulations and does not need an artificial outflow boundary condition. It does conserve mass. Moreover, optimal-order error estimates for ELLAM have been obtained. In contrast, many methods have only suboptimal-order estimates when applied to solve these problems. Furthermore, our ELLAM scheme provides a systematic approach to treat the interface problems of advection-type equations and can be naturally combined with domain decomposition and local refinement techniques to solve these problems. Numerical results in one and two dimensions are presented and discussed.
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Communicated by S. N. Atluri, December 1, 1992
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Ewing, R.E., Wang, H. Eulerian-Lagrangian localized adjoint methods for linear advection or advection-reaction equations and their convergence analysis. Computational Mechanics 12, 97–121 (1993). https://doi.org/10.1007/BF00370489
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DOI: https://doi.org/10.1007/BF00370489