Abstract
This chapter is devoted to the approximation of time-dependent PDEs by finite elements. An exhaustive review of this vast subject goes beyond the scope of this book; therefore, we restrict ourselves to illustrating some important concepts. In particular, we emphasize the method of lines where the problem is first approximated in space, yielding a system of coupled ordinary differential equations, and then a time-marching algorithm is employed to construct the time-approximation.
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© 2004 Springer Science+Business Media New York
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Ern, A., Guermond, JL. (2004). Time-Dependent Problems. In: Theory and Practice of Finite Elements. Applied Mathematical Sciences, vol 159. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4355-5_6
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DOI: https://doi.org/10.1007/978-1-4757-4355-5_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1918-2
Online ISBN: 978-1-4757-4355-5
eBook Packages: Springer Book Archive