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Mathematically Founded Design of Adaptive Finite Element Software

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Multiscale and Adaptivity: Modeling, Numerics and Applications

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2040))

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Abstract

In these lecture notes we derive from the mathematical concepts of adaptive finite element methods basic design principles of adaptive finite element software. We introduce finite element spaces, discuss local refinement of simplical grids, the assemblage and structure of the discrete linear system, the computation of the error estimator, and common adaptive strategies. The mathematical discussion naturally leads to appropriate data structures and efficient algorithms for the implementation. The theoretical part is complemented by exercises giving an introduction to the implementation of solvers for linear and nonlinear problems in the adaptive finite element toolbox ALBERTA.

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  1. Institut für Angewandte Analysis und Numerische Simulation, Fachbereich Mathematik, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Kunibert G. Siebert

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Siebert, K.G. (2011). Mathematically Founded Design of Adaptive Finite Element Software. In: Multiscale and Adaptivity: Modeling, Numerics and Applications. Lecture Notes in Mathematics(), vol 2040. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24079-9_4

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