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

11/15/2022

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by   Franco Dassi, et al.

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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:=-Δ^2 u and to search the main uknown u in the H^2∩ H_0^1 Sobolev space. The virtual element discretization is well possed on a C^1× C^0 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.