Kirk Lecture: A Recent Technology for Scientific Computing - The Virtual Element Method

Explore the Virtual Element Method (VEM), a cutting-edge technology for solving boundary value problems in Partial Differential Equations, in this 54-minute Kirk Lecture by Professor Donatella Marini. Discover how VEM generalizes the Finite Element Method (FEM) by allowing decompositions into polygons and polyhedra of various shapes, offering enhanced accuracy, efficiency, and flexibility in scientific computing. Learn about the growing interest in polytopal meshes and their potential for improved computational efficiency compared to traditional grids. Gain insights into the basic concepts of conforming VEM through a simple model problem, and examine numerical results for complex two- and three-dimensional applications. Conclude with an introduction to Serendipity versions, which significantly reduce degrees of freedom and the size of the final linear system.