A semi-nonconforming Virtual Element Method for curved domains in three dimensions
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In this talk, we discuss a semi-nonconforming Virtual Element Method for curved domains in three dimensions. Virtual Element Methods were introduced in [1] and are well known for their ability to efficiently handle polygonal and polyhedral meshes of general shape. In the three-dimensional setting, the construction of a virtual element space [2] requires first defining suitable virtual spaces on each face and subsequently extending them to the interior of the element. This procedure becomes particularly challenging when dealing with domains with curved faces. By contrast, nonconforming virtual element methods [3] admit a more natural extension to three dimensions and are more manageable in the presence of curved elements. In this talk, we present a virtual element formulation in which elements possess planar faces that are conforming in the interior of the domain, while curved boundary faces are treated in a nonconforming manner. We also present numerical experiments illustrating the performance of the method, including tests involving both Dirichlet and Neumann boundary conditions.
