Abstract
The calculation of accurate finite element approximations to the solutions of elliptic boundary value problems in two dimensions can readily be achieved, and theoretical bounds on the finite element error can be obtained, when the boundary and boundary conditions are sufficiently smooth. However, when the boundary contains a re-entrant corner, so that the solution contains a singularity, accuracy is lost. The usual error analysis is also not applicable since the solution no longer has the required differentiability properties. Methods are described for overcoming this difficulty and for producing approximations to the stress function,to the displacements and to the stress concentration factor.
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Whiteman, J.R., Schiff, B. (1976). Finite Element Approximation of Singular Functions. In: Collatz, L., Werner, H., Meinardus, G. (eds) Numerische Methoden der Approximationstheorie/Numerical Methods of Approximation Theory. International Series of Numerical Mathematics, vol 30. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7692-6_16
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DOI: https://doi.org/10.1007/978-3-0348-7692-6_16
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-0824-7
Online ISBN: 978-3-0348-7692-6
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