Russell, T. F. Eulerian-Langrangian localized adjoint methods for advection-dominated problems. (English) Zbl 0694.76037 Numerical analysis, Proc. 13th Biennial Conf., Dundee/UK 1989, Pitman Res. Notes Math. Ser. 228, 206-228 (1990). Summary: [For the entire collection see Zbl 0689.00014.] Eulerian-Lagrangian localized adjoint methods (ELLAM), are a space-time finite-element methodology that builds on concepts of tracking advection- dominated flows (Eulerian-Lagrangian methods, or ELM) and of optimal test functions (adjoint methods). The ELLAM development yields a conservative scheme that treats boundary conditions systematically and generalizes ELM, thus overcoming the two principal shortcomings of ELM while maintaining the numerical advantages. A single formulation handles advection-diffusion and pure advection problems without upwinding or artificial boundary conditions. For the simplest case, this paper presents the formulation and some numerical results that confirm the potential of the approach. Cited in 3 Documents MSC: 76R50 Diffusion 76M99 Basic methods in fluid mechanics 65N99 Numerical methods for partial differential equations, boundary value problems Keywords:Eulerian-Lagrangian localized adjoint methods; space-time finite-element methodology; tracking advection-dominated flows; Eulerian-Lagrangian methods; optimal test functions; advection-diffusion Citations:Zbl 0689.00014 PDFBibTeX XML