PREPRINT

A virtual element method on polyhedral meshes for the sixth-order elliptic problem

Franco Dassi, David Mora, Carlos Reales, Ivàn Velàsquez

Submitted on 15 November 2022

Abstract

In this work we analyze a virtual element method on polyhedral meshes for solving the sixth-order elliptic problem with simply supported boundary conditions. We apply the Ciarlet-Raviart arguments to introduce an auxiliary unknown σ:=Δ2u and to search the main uknown u in the H2H01 Sobolev space. The virtual element discretization is well possed on a C1×C0 virtual element spaces. We also provide the convergence and error estimates results. Finally, we report a series of numerical tests to verify the performance of numerical scheme.

Preprint

Comment: 20 pages 5 figures

Subjects: Mathematics - Numerical Analysis; 65M99

URL: http://arxiv.org/abs/2211.07953