Dietmar Gallistl, Moritz Hauck, Yizhou Liang, Daniel Peterseim
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Mixed finite elements for the Gross–Pitaevskii eigenvalue problem: a priori error analysis and guaranteed lower energy bound
We establish an a priori error analysis for the lowest-order Raviart–Thomas finite element discretization of the nonlinear Gross-Pitaevskii eigenvalue problem. Optimal convergence rates are obtained for the primal and dual variables as well as for the eigenvalue and energy approximations. In contrast to conforming approaches, which naturally imply upper energy bounds, the proposed mixed discretization provides a guaranteed and asymptotically exact lower bound for the ground state energy. The theoretical results are illustrated by a series of numerical experiments.
期刊介绍:
The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects. Occasional survey articles are also published.