scholarly journals A Study on Anisotropic Mesh Adaptation for Finite Element Approximation of Eigenvalue Problems with Anisotropic Diffusion Operators

2015 ◽  
Vol 37 (6) ◽  
pp. A2924-A2946 ◽  
Author(s):  
Jingyue Wang ◽  
Weizhang Huang
Keyword(s):  
Finite Element ◽  
Anisotropic Diffusion ◽  
Eigenvalue Problems ◽  
Finite Element Approximation ◽  
Mesh Adaptation ◽  
Element Approximation ◽  
Anisotropic Mesh ◽  
Anisotropic Mesh Adaptation

scholarly journals Regularity and hp discontinuous Galerkin finite element approximation of linear elliptic eigenvalue problems with singular potentials

2019 ◽  
Vol 29 (08) ◽  
pp. 1585-1617 ◽  
Author(s):  
Yvon Maday ◽  
Carlo Marcati
Keyword(s):  
Finite Element ◽  
Discontinuous Galerkin ◽  
Sobolev Spaces ◽  
Eigenvalue Problems ◽  
Weighted Sobolev Spaces ◽  
Finite Element Approximation ◽  
Three Dimensions ◽  
Element Approximation ◽  
Singular Potentials ◽  
Dg Method

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.

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