Kaland, Lena; Roos, Hans-Görg Parabolic singularly perturbed problems with exponential layers: robust discretizations using finite elements in space on Shishkin meshes. (English) Zbl 1195.65121 Int. J. Numer. Anal. Model. 7, No. 3, 593-606 (2010). Summary: A parabolic initial-boundary value problem with solutions displaying exponential layers is solved using layer-adapted meshes. The paper combines finite elements in space, i.e., a pure Galerkin technique on a Shishkin mesh, with some standard discretizations in time. We prove error estimates as well for the \(\theta \)-scheme as for discontinuous Galerkin in time. Cited in 8 Documents MSC: 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 65M06 Finite difference methods 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 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs Keywords:convection-diffusion equation; Shishkin mesh; time discretization; semidiscretization; theta-scheme in time; numerical example; parabolic initial-boundary value problem; exponential layers; finite elements in space; error estimates; discontinuous Galerkin in time PDFBibTeX XMLCite \textit{L. Kaland} and \textit{H.-G. Roos}, Int. J. Numer. Anal. Model. 7, No. 3, 593--606 (2010; Zbl 1195.65121) Full Text: Link