Basic Principles of axial-symmetric Virtual Element Method
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There are several three-dimensional numerical simulations whose solutions are characterized by axial symmetry, such as the design of wind instrument mouth- pieces, the analysis of pressure vessels, the study of flow in pipes and nozzles, or the computation of electromagnetic fields in coils. Since assembling and solving a three-dimensional problem is, in general, compu- tationally expensive, it is possible to exploit the axial symmetry of the solution to reduce these problems to a two-dimensional formulation. In this talk, we introduce a novel virtual element space specifically designed for axisymmetric problems, whose construction is based on the use of weighted Sobolev spaces. Numerical experiments demonstrate the good approximation properties of the proposed method.
