Zítka, Martin; Segeth, Karel; Šolín, Pavel Higher-order FEM for a system of nonlinear parabolic PDE’s in 2D with a-posteriori error estimates. (English) Zbl 1056.65091 Feistauer, M. (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2003, the 5th European conference on numerical mathematics and advanced applications, Prague, Czech Republic, August 18–22, 2003. Berlin: Springer (ISBN 3-540-21460-7/hbk). 854-863 (2004). Summary: Initial-boundary value problems for systems of nonlinear parabolic partial differential equations arise in many important practical applications in electromagnetics, chemistry, modelling of diffusion and heat transfer processes and other fields. We are concerned with their solution by means of the method of lines with higher-order finite element spatial discretization on unstructured triangular meshes. Obviously, development of realistic a posteriori error estimates plays an essential role in the application of a strategy of this type.For the entire collection see [Zbl 1046.65002]. MSC: 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs 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 35K55 Nonlinear parabolic equations 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs Keywords:numerical examples; initial-boundary value problems; systems of nonlinear parabolic partial differential equations; method of lines; finite element; unstructured triangular meshes; error estimates PDFBibTeX XMLCite \textit{M. Zítka} et al., in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2003, the 5th European conference on numerical mathematics and advanced applications, Prague, Czech Republic, August 18--22, 2003. Berlin: Springer. 854--863 (2004; Zbl 1056.65091)