A posteriori error estimates for a Virtual Elements Method for the Steklov eigenvalue problem

2016/09/22 by Mora, David, Rivera, Gonzalo, Rodríguez, Rodolfo · 6 citations
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1609.07154

Abstract

The paper deals with the a posteriori error analysis of a virtual element method for the Steklov eigenvalue problem. The virtual element method has the advantage of using general polygonal meshes, which allows implementing very efficiently mesh refinement strategies. We introduce a residual type a posteriori error estimator and prove its reliability and efficiency. We use the corresponding error estimator to drive an adaptive scheme. Finally, we report the results of a couple of numerical tests, that allow us to assess the performance of this approach.

Cited by

• A locking-free mixed virtual element discretization for the two dimensional elasticity eigenvalue problem
• A stabilized virtual element framework for the steady state Boussinesq equation with temperature-dependent parameters
• Deep Eigenspace Network for Parametric Non-self-adjoint Eigenvalue Problems
• A virtual element approximation for the modified transmission eigenvalues for natural materials
• Finite element analysis of an eigenvalue problem arising from neutron transport
• A posteriori error estimates for a C¹ virtual element method applied to the thin plate vibration problem

Related

• A virtual element method for the Steklov eigenvalue problem allowing small edges
• A posteriori error estimates for the virtual element method
• An adaptive algorithm based on the shifted inverse iteration for the Steklov eigenvalue problem
• Adaptive virtual elements based on hybridized, reliable, and efficient flux reconstructions
• Some Error Analysis on Virtual Element Methods