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A \(C^1\)–\(C^0\) virtual element discretization for a sixth-order elliptic equation

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Abstract

In this paper we study a virtual element method for the sixth-order elliptic problem with clamped and simply supported boundary conditions type. Using arguments like Ciarlet-Raviart method we introduce an auxiliary unknown \(w:=\Delta u\) and we propose a weak formulation on \(H^2\times H^1\) Sobolev space. A \(C^1\times C^0\) virtual element discretization is proposed to approximate the solutions of the weak formulation. We also provide the convergence and error estimates results. Finally, several numerical examples illustrating the performance of the virtual element method are reported.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Córdoba, Montería, Colombia

    José Causil & Carlos Reales

  2. Facultad de Ciencias Básicas, Universidad del Sinú E.B.Z., Montería, Colombia

    Iván Velásquez

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  1. José Causil
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  2. Carlos Reales
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  3. Iván Velásquez
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Correspondence to Iván Velásquez.

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Causil, J., Reales, C. & Velásquez, I. A \(C^1\)–\(C^0\) virtual element discretization for a sixth-order elliptic equation. Calcolo 59, 39 (2022). https://doi.org/10.1007/s10092-022-00482-5

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