Abstract
For functions u ∈ H 1(Ω) in an open, bounded polyhedron \(\varOmega \subset \mathbb{R}^{d}\) of dimension d = 1, 2, 3, which are analytic in \(\overline{\varOmega }\setminus \mathcal{S}\) with point singularities concentrated at the set \(\mathcal{S}\subset \overline{\varOmega }\) consisting of a finite number of points in \(\overline{\varOmega }\), the exponential rate \(\exp (-b\root{d + 1}\of{N})\) of convergence of h p-version continuous Galerkin finite element methods on families of regular, simplicial meshes in Ω can be achieved. The simplicial meshes are assumed to be geometrically refined towards \(\mathcal{S}\) and to be shape regular, but are otherwise unstructured.
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This work is supported by grant ERC AdG STAHDPDE 247277.
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Schwab, C. (2015). Exponential Convergence of Simplicial h p-FEM for H 1-Functions with Isotropic Singularities. In: Kirby, R., Berzins, M., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham. https://doi.org/10.1007/978-3-319-19800-2_40
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DOI: https://doi.org/10.1007/978-3-319-19800-2_40
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