Abstract
The finite element method defines a general concept for systematically constructing finite-dimensional subspaces of Sobolev spaces that lead to discretizations of weak formulations of partial differential equations or minimization problems. The approximation properties of low-order finite element functions on simplicial meshes and their application to stationary and evolutionary linear model problems are discussed in this chapter. Short Matlab implementations illustrate the flexibility of the method and provide a tool to verify theoretical statements.
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Bartels, S. (2015). FEM for Linear Problems. In: Numerical Methods for Nonlinear Partial Differential Equations. Springer Series in Computational Mathematics, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-13797-1_3
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DOI: https://doi.org/10.1007/978-3-319-13797-1_3
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