Kirk Lecture: A recent technology for Scientific Computing: the Virtual Element Method

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• Donatella Marini (Università degli Studi di Pavia; Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI))
• Monday 21 October 2019, 16:00-17:00
• Seminar Room 1, Newton Institute.

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GCS - Geometry, compatibility and structure preservation in computational differential equations

The Virtual Element Method (VEM) is a recent technology for the numerical solution of boundary value problems for Partial Differential Equations. It could be seen as a generalization of the Finite Element Method (FEM). With FEM the computational domain is typically split in triangles/quads (tetrahedra/hexahedra). VEM responds to the recent interest in using decompositions into polygons/polyhedra of very general shape, whenever more convenient for the approximation of problems of practical interest. Indeed,the possibility of using general polytopal meshes opens up a new range of opportunities in terms of accuracy, efficiency and flexibility. This is for instance reflected by the fact that various (commercial and free) codes recently included and keep developing polytopal meshes, showing in selected applications an improved computational efficiency with respect to tetrahedral or hexahedral grids. In this talk, after a general description of the use and potential of Scientific Computing, basic ideas of conforming VEM will be described on a simple model problem. Numerical results on more general problems in two and three dimension will be shown. Hints on Serendipity versions will be given at the end. These procedures allow to decrease significantly the number of degrees of freedom, that is, to reduce the dimension of the final linear system.

This talk is part of the Isaac Newton Institute Seminar Series series.

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