Steklov特征值问题间断有限元自适应方法
Discontinuous Finite Element Adaptive Method for Steklov Eigenvalue Problems
DOI: 10.12677/AAM.2022.1111805, PDF,    科研立项经费支持
作者: 陈兴龙：贵州师范大学数学科学学院，贵州 贵阳
关键词: Steklov特征值；间断有限元；自适应方法；Steklov Eigenvalue； Discontinuous Galerkin； Self-Adaption Method
摘要: 本文研究了Steklov特征值问题的自适应间断有限元法。我们推导了相应的离散格式并给出了特征值的后验误差估计子。通过构造辅助的泡泡函数和提升算子，我们证明了后验误差估计子的可靠性和有效性。此外，我们通过数值实验验证了后验误差估计子在自适应网格下的鲁棒性。
Abstract: This paper studies the eigenvalue problem of adaptive discontinuous finite element method (fem). We derive the corresponding discrete format and give the posterior error estimators of the eigen-values. By constructing auxiliary bubble functions and lifting operators, we prove the reliability and validity of the posterior error estimator. In addition, we verify the robustness of the posterior error estimator under the adaptive grid through numerical experiments.
文章引用：陈兴龙. Steklov特征值问题间断有限元自适应方法[J]. 应用数学进展, 2022, 11(11): 7607-7615. https://doi.org/10.12677/AAM.2022.1111805

参考文献

[1] Bergman, S. and Schiffffer, M. (1953) Kernel Functions and Elliptic Differential Equations in Mathematical Physics. Pure and Applied Mathematics 4, Academic Press, New York.
[2] Zeng, Y. and Wang, F. (2017) A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Steklov Eigenvalue Problems. Applied Mathematics, 62, 243-267. [Google Scholar] [CrossRef] 
[3] Cockburn, B., Karniadakis, G.E. and Shu, C.W. (1999) Discontinuous Galerkin Methods, Thoery, Computation and Applications. Springer-Verlag, Berlin. [Google Scholar] [CrossRef] 
[4] Antonietti, P., Buffa, A. and Perugia, I. (2006) Discontinuous Galerkin Approximation of the Laplace Eigenproblem. Computer Methods in Applied Mechanics and Engineering, 195, 3483-3503. [Google Scholar] [CrossRef] 
[5] Wang, L., Xiong, C., Wu, H. and Luo, F. (2019) A Priori and a Posteriori Error Analysis for Discontinuous Galerkin Finite Element Approximations of Biharmonic Eigen-value Problems. Advances in Computational Mathematics, 45, 2623-2646. [Google Scholar] [CrossRef] 
[6] Buffa, A. and Perugia, I. (2006) Discontinuous Galerkin Ap-proximation of the Maxwell Eigenproblem. SIAM Journal on Numerical Analysis, 44, 2198-2226. [Google Scholar] [CrossRef] 
[7] Li, Y.J., Bi, H. and Yang, Y.D. (2022) The a Priori and a Posteriori Error Estimates of DG Method for the Steklov Eigenvalue Problem in Inverse Scattering. Journal of Scientific Computing, 32, 2-10.

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