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SUMMARY:Kirk Lecture:  A recent technology for Scientific Computing: the V
 irtual Element Method - Donatella Marini (Università degli Studi di Pavia
 \; Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI))
DTSTART:20191021T150000Z
DTEND:20191021T160000Z
UID:TALK132433@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The Virtual Element Method (VEM) is a recent technology for th
 e numerical solution of boundary value problems for Partial Differential E
 quations. It could be seen as a generalization of the Finite Element Metho
 d (FEM). With FEM the computational domain is typically split in triangles
 /quads (tetrahedra/hexahedra). VEM responds to the recent interest in usin
 g decompositions into polygons/polyhedra of very general shape\, whenever 
 more convenient for the approximation of problems of practical interest. I
 ndeed\,the possibility of using general polytopal meshes opens up a new ra
 nge of opportunities in terms of accuracy\, efficiency and flexibility. Th
 is is for instance reflected by the fact that various (commercial and free
 ) codes recently included and keep developing polytopal meshes\, showing i
 n selected applications an improved computational efficiency with respect 
 to tetrahedral or hexahedral grids. In this talk\, after a general descrip
 tion of the use and potential of Scientific Computing\, basic ideas of con
 forming 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 t
 o decrease significantly the number of degrees of freedom\, that is\, to r
 educe the dimension of the final linear system.
LOCATION:Seminar Room 1\, Newton Institute
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