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Symmetric error estimates for moving mesh Galerkin methods for advection-diffusion equations. (English) Zbl 1025.65051

The authors use the moving mesh Galerkin method to study the approximate solution of advection-diffusion equation with mixed boundary conditions. A continuous-time moving mesh is defined in terms of a ”convected-time” derivative. Symmetric error bounds are given for the continuous-time case and the discrete-time one. Also two optimal order \(L^2\) error bounds are presented. The paper effectively combines ideas of T. Dupont [Math. Comput. 39, 85–107 (1982; Zbl 0493.65044)], R. E. Bank and R. F. Santos [SIAM J. Numer. Anal. 30, 1–18 (1993; Zbl 0770.65060)], and J. Douglas jun. and T. F. Russel [SIAM J. Numer. Anal. 19, 871–885 (1982; Zbl 0492.65051)].

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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