Eriksson, Kenneth; Estep, Don; Hansbo, Peter; Johnson, Claes Introduction to computational methods for differential equations. (English) Zbl 0843.65057 Ainsworth, M. (ed.) et al., Advances in numerical analysis. Vol. IV. Theory and numerics of ordinary and partial differential equations. Proceedings of the sixth SERC summer school in numerical analysis, Leicester, UK, July 18-29, 1994. Oxford: Clarendon Press. Oxford Science Publications. 77-122 (1995). Summary: We give an introduction to a unified approach to computational methods for differential equations based on Galerkin methods with piecewise polynomial approximation. We present adaptive methods with reliable and efficient control of computational errors and also discuss estimation and control of data and modeling errors. As model problems we consider two-point boundary value problems, initial value problems for ordinary differential equations, the Poisson equation and the heat equation. We present sample results using the Femlab software.For the entire collection see [Zbl 0836.00040]. Cited in 9 Documents MSC: 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 34B15 Nonlinear boundary value problems for ordinary differential equations 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35K05 Heat equation Keywords:finite element method; survey paper; Galerkin methods; adaptive methods; Poisson equation; heat equation PDFBibTeX XMLCite \textit{K. Eriksson} et al., in: Advances in numerical analysis. Vol. IV. Theory and numerics of ordinary and partial differential equations. Proceedings of the sixth SERC summer school in numerical analysis, Leicester, UK, July 18-29, 1994. Oxford: Clarendon Press. 77--122 (1995; Zbl 0843.65057)