H1-conforming virtual element method for the Laplacian eigenvalue problem in mixed form
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS(2024)
Abstract
In this paper, we propose the Stokes-type virtual element method for the Laplacian eigenvalue problem in mixed form, in which the eigenvalue problem is reformulated in terms of the velocity and the pressure of the Darcy flow. The virtual element method is H1-conforming and divergence-free. By applying these properties, the inf-sup condition and the spectral approximation theory of compact operator, we derive the optimal a priori error estimates. Then we focus on the a posteriori error estimates. Based on the superconvergence analysis, the Helmholtz decomposition and the properties of bubble functions, we prove the upper and lower bounds of the residual-type a posteriori error estimator with respect to the approximation error. Finally some numerical results are given to validate the theoretical analysis and present the good performance of the adaptive algorithm.& COPY; 2023 Elsevier B.V. All rights reserved.
MoreTranslated text
Key words
Stokes -type virtual element method,Self-adjoint elliptic eigenvalue problem,Superconvergence Analysis,A priori and a posteriori error estimates
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined