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

2022/11/15 by Dassi, Franco, Mora, David, Reales, Carlos +1
#65M99 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2211.07953

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:=-Δ² u and to search the main uknown u in the H²∩ H₀¹ 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.

Related

• Virtual Element Methods for general second order elliptic problems on polygonal meshes
• Mixed Virtual Element Methods for general second order elliptic problems on polygonal meshes
• A C⁰ finite element algorithm for the sixth order problem with simply supported boundary conditions
• Serendipity Virtual Elements on Polyhedral Meshes
• Virtual Element Method for Quasilinear Elliptic Problems