Apel, Th.; Berzins, M.; Jimack, P. K.; Kunert, G.; Plaks, A.; Tsukerman, I.; Walkley, M. Mesh shape and anisotropic elements: Theory and practice. (English) Zbl 0959.65128 Whiteman, J. R. (ed.), The mathematics of finite elements and applications X, MAFELAP 1999. Proceedings of the 10th conference, Brunel Univ., Uxbridge, Middlesex, GB, June 22-25, 1999. Amsterdam: Elsevier. 367-376 (2000). Summary: The relationship between the shape of finite elements in unstructured meshes and the error that results in the numerical solution is of increasing importance as finite elements are used to solve problems with highly anisotropic and, often, very complex solutions. This issues is explored in terms of a priori and a posteriori error estimates, and through consideration of the practical issues associated with assessing element shape quality and implementing an adaptive finite element solver.For the entire collection see [Zbl 0942.00044]. Cited in 5 Documents MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 35L50 Initial-boundary value problems for first-order hyperbolic systems Keywords:anisotropic finite elements; element shape; maximum angle condition; unstructured meshes; a priori and a posteriori error estimates PDFBibTeX XMLCite \textit{Th. Apel} et al., in: The mathematics of finite elements and applications X, MAFELAP 1999. Proceedings of the 10th conference, Brunel Univ., Uxbridge, Middlesex, GB, June 22--25, 1999. Amsterdam: Elsevier. 367--376 (2000; Zbl 0959.65128)