Virtual element methods for fourth-order problems

• Date: 16. 2. 2023
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K3
• Speaker: Alice Hodson

In recent years, the discretisation of partial differential equations via the virtual element method (VEM) has seen a rapid increase. The virtual element method is an extension of both finite element and mimetic finite difference methods. VEM spaces can be easily constructed to enforce desirable properties of the discrete functions even on general polygonal meshes, which makes the approach very appealing for a vast range of problems. The construction of even a lowest order C^1-conforming space is not straightforward within the standard finite element setting and higher order nonconforming spaces suitable for fourth-order problems are also not readily available. In this talk, we develop a generic approach for constructing the necessary projection operators, virtual element spaces, and discrete forms. We analyse these VEMs before looking at their application to a wide range of fourth-order problems.