Abstract
Finite element methods (FEM) were used very early for problems in structural mechanics. Such problems often have a natural discretization by partitioning the structure in a number of finite elements, and this gave the name to this class of methods. This kind of mechanical approach merged with the more mathematical approach that gained momentum in the 1960s.
FEM are more flexible than finite difference methods in the sense that irregular domains can more easily be represented accurately. In this chapter we shall discuss boundary and initial-boundary value problems, and in the latter case assume that finite difference methods are used for discretization in time.
In the final section we discuss discontinuous Galerkin methods (DG), which have become very popular recently. They are closely connected to FEM, and are therefore included in this chapter, even if they could be considered as a separate class of methods by themselves.
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References
Hesthaven, J.S., Warburton, T.: Nodal Discontinuous Galerkin Methods. Algorithms, Analysis, and Applications. Texts in Applied Mathematics, vol. 54. Springer, Berlin (2008)
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© 2011 Springer-Verlag Berlin Heidelberg
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Gustafsson, B. (2011). Finite Element Methods. In: Fundamentals of Scientific Computing. Texts in Computational Science and Engineering, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19495-5_11
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DOI: https://doi.org/10.1007/978-3-642-19495-5_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19494-8
Online ISBN: 978-3-642-19495-5
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