In this paper we study a C1 Virtual Element Method (VEM) on polyhedral meshes for bi-harmonic eigenvalue problems in three dimensions. Optimal order error estimates for the eigenfunctions and a double order for the eigenvalues are obtained by using the approximation theory of compact self-adjoint operators. Finally, a set of tests will numerically prove the theoretical result of the proposed scheme.
Dassi, F., Velasquez, I. (2022). Virtual element method on polyhedral meshes for bi-harmonic eigenvalues problems. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 121(1 September 2022), 85-101 [10.1016/j.camwa.2022.07.001].
Virtual element method on polyhedral meshes for bi-harmonic eigenvalues problems
Dassi, F
;
2022
Abstract
In this paper we study a C1 Virtual Element Method (VEM) on polyhedral meshes for bi-harmonic eigenvalue problems in three dimensions. Optimal order error estimates for the eigenfunctions and a double order for the eigenvalues are obtained by using the approximation theory of compact self-adjoint operators. Finally, a set of tests will numerically prove the theoretical result of the proposed scheme.
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