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

DOI10.1142/S0218202519500295zbMath1431.65209arXiv1810.09010MaRDI QIDQ4973293

Carlo Marcati, Yvon Maday

Publication date: 3 December 2019

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.09010

zbMATH Keywords

weighted Sobolev spacesSchrödinger equationelliptic eigenvalue problemelliptic regularitydiscontinuous Galerkin\(hp\) graded finite element method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Smoothness and regularity of solutions to PDEs (35B65) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Schrödinger operator, Schrödinger equation (35J10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Direct numerical methods for linear systems and matrix inversion (65F05) Preconditioners for iterative methods (65F08)

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Uses Software

• SLEPc
• deal.ii
• PETSc
• BiCGstab
• JDQZ

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