Analysis of Schrödinger operators with inverse square potentials. II: FEM and approximation of eigenfunctions in the periodic case. (English) Zbl 1390.65145
Summary: In this article, we consider the problem of optimal approximation of eigenfunctions of Schrödinger operators with isolated inverse square potentials and of solutions to equations involving such operators. It is known in this situation that the finite element method performs poorly with standard meshes. We construct an alternative class of graded meshes, and prove and numerically test optimal approximation results for the finite element method using these meshes. Our numerical tests are in good agreement with our theoretical results in the first part [E. Hunsicker et al., Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 55(103), No. 2, 157–178 (2012; Zbl 1299.35055)].
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35B10 | Periodic solutions to PDEs |
| 35J10 | Schrödinger operator, Schrödinger equation |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
Citations:
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