CSCDR Seminar - Seulip Lee (UGA)
When: Wednesday,
October 4, 2023
2:00 PM
-
3:00 PM
Where: > See description for location
Description: Zoom link: https://umassd.zoom.us/j/99682538143?pwd=VURjV0luZDg4QngwVlByaDVKOFd5UT09
Title: Edge-averaged virtual element methods for convection-dominated problems
Abstract: We propose edge-averaged virtual element (EAVE) methods for convection-diffusion problems in the convection-dominated regime. In finite element methods, the edge-averaged finite element (EAFE) scheme is a monotone discretization on Delaunay triangulations. With monotonicity property, the EAFE method guarantees stable numerical solutions to convection-dominated problems. Therefore, we aim to generalize the EAFE stabilization to the virtual element methods (VEMs). One resulting EAVE method is monotone on a Voronoi mesh with a dual Delaunay triangulation of acute triangles. The Bernoulli function and the geometric data of the Voronoi mesh readily compute the bilinear form in the monotone method, whose stiffness matrix is an M-matrix. Moreover, we present a general framework for EAVE methods, presenting another EAVE bilinear form that includes the stiffness matrix of the lowest-order virtual element method for the Poisson equation. The bilinear form in this framework works with general polygonal meshes and leads to a sufficient condition for the monotonicity property.
Title: Edge-averaged virtual element methods for convection-dominated problems
Abstract: We propose edge-averaged virtual element (EAVE) methods for convection-diffusion problems in the convection-dominated regime. In finite element methods, the edge-averaged finite element (EAFE) scheme is a monotone discretization on Delaunay triangulations. With monotonicity property, the EAFE method guarantees stable numerical solutions to convection-dominated problems. Therefore, we aim to generalize the EAFE stabilization to the virtual element methods (VEMs). One resulting EAVE method is monotone on a Voronoi mesh with a dual Delaunay triangulation of acute triangles. The Bernoulli function and the geometric data of the Voronoi mesh readily compute the bilinear form in the monotone method, whose stiffness matrix is an M-matrix. Moreover, we present a general framework for EAVE methods, presenting another EAVE bilinear form that includes the stiffness matrix of the lowest-order virtual element method for the Poisson equation. The bilinear form in this framework works with general polygonal meshes and leads to a sufficient condition for the monotonicity property.
Contact: > See Description for contact information
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