Regularity and hp discontinuous Galerkin finite element approximation of linear elliptic eigenvalue problems with singular potentials
2019 ◽
Vol 29
(08)
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pp. 1585-1617
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Keyword(s):
We study the regularity in weighted Sobolev spaces of Schrödinger-type eigenvalue problems, and we analyze their approximation via a discontinuous Galerkin (dG) [Formula: see text] finite element method. In particular, we show that, for a class of singular potentials, the eigenfunctions of the operator belong to analytic-type non-homogeneous weighted Sobolev spaces. Using this result, we prove that an isotropically graded [Formula: see text] dG method is spectrally accurate, and that the numerical approximation converges with exponential rate to the exact solution. Numerical tests in two and three dimensions confirm the theoretical results and provide an insight into the behavior of the method for varying discretization parameters.
1992 ◽
Vol 43
(3)
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pp. 291-311
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2013 ◽
Vol 51
(4)
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pp. 2088-2106
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2006 ◽
Vol 44
(6)
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pp. 2650-2670
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2009 ◽
Vol 31
(1)
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pp. 254-280
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2005 ◽
Vol 25
(4)
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pp. 726-749
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2019 ◽
Vol 80
(2)
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pp. 993-1018
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2015 ◽
Vol 93
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pp. 206-214
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2014 ◽
Vol 52
(2)
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pp. 993-1016
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2002 ◽
Vol 36
(1)
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pp. 1-32
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2009 ◽
Vol 47
(4)
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pp. 2660-2685
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