Dupont, Todd F.; Liu, Yingjie Symmetric error estimates for moving mesh Galerkin methods for advection-diffusion equations. (English) Zbl 1025.65051 SIAM J. Numer. Anal. 40, No. 3, 914-927 (2002). 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)]. Reviewer: Emil Minchev (Chiba) Cited in 14 Documents 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 Keywords:Galerkin methods; parabolic equations; finite element; moving mesh; advection-diffusion equation; error bounds Citations:Zbl 0493.65044; Zbl 0770.65060; Zbl 0492.65051 PDFBibTeX XMLCite \textit{T. F. Dupont} and \textit{Y. Liu}, SIAM J. Numer. Anal. 40, No. 3, 914--927 (2002; Zbl 1025.65051) Full Text: DOI