Bibliographic Details
| Title: |
Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation. |
| Authors: |
Heid, Pascal1 (AUTHOR) pascal.heid@maths.ox.ac.uk, Stamm, Benjamin2 (AUTHOR) best@acom.rwth-aachen.de, Wihler, Thomas P.3 (AUTHOR) thomas.wihler@math.unibe.ch |
| Source: |
Journal of Computational Physics. Jul2021, Vol. 436, pN.PAG-N.PAG. 1p. |
| Subjects: |
Gross-Pitaevskii equations, Degrees of freedom, Elliptic operators |
| Abstract: |
• Numerical approximation of the ground state of the Gross-Pitaevskii equation. • Introduction of a novel mesh refinement technique based on local energy reductions. • Adaptive interplay of a gradient ow iteration and the novel mesh refinemen method. • Optimal convergence rate with respect to the degrees of freedom in the test problems. We present an effective adaptive procedure for the numerical approximation of the steady-state Gross–Pitaevskii equation. Our approach is solely based on energy minimization, and consists of a combination of a novel adaptive finite element mesh refinement technique, which does not rely on any a posteriori error estimates, and a recently proposed new gradient flow. Numerical tests show that this strategy is able to provide highly accurate results, with optimal convergence rates with respect to the number of degrees of freedom. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
