Thursday, March 1, 2018 - 14:00
Weierstraß-Institut
Mohrenstr. 39, 10117 Berlin, Erhard-Schmidt-Hörsaal, Erdgeschoss
Seminar Numerische Mathematik
The Virtual Element Method is a novel way to discretize a partial differential equation. It avoids the explicit integration of shape functions and introduces an innovative construction of the stiffness matrix so that it acquires very interesting properties and advantages. One among them is the possibility to apply the VEM to general polygonal/polyhedral domain decomposition, also characterized by non-conforming and non-convex elements.
In this talk we focus on the definition/construction of the Virtual Element functional spaces in three dimensions and how apply this new strategy to set a standard Laplacian problem in 3D.
Finally we test the method to show its robustness with respect to element distortion and the polynomial approximation degree $k$. Then, we move to more involved cases: convection-diffusion-reaction problems with variable coefficients and magnetostatic Maxwell equations.
submitted by lawrenz (marion.lawrenz@wias-berlin.de, 030 20372566)