Calendar

Posted June 23, 2026

Computational Mathematics Seminar

Rekha Khot, IIT Palakkad, Kerala, India
Virtual Element Methods for Plate Bending and Coupled Poroelastic Problems

Traditionally, the finite element analysis relies on meshes composed of simplicial elements (triangles in 2D and tetrahedra in 3D). Over the past decade, significant progress has been made in the development of discretization techniques based on polytopal meshes (polygonal in 2D and polyhedral in 3D), motivated by their flexibility in handling complex geometries, adaptive mesh refinement, and a unified framework. Among several approaches, this talk focuses on the Virtual Element Method (VEM). Thin plate models are governed by fourth-order PDEs. We first discuss conforming and nonconforming VEM for a simple biharmonic problem. In particular, we present various smoothing operators that connect nonconforming spaces to conforming ones, enabling the treatment of a discrete rough source term and/or the quantification of nonconformity error. We then consider a coupled mixed-dimensional (3D–2D) bulk–surface model describing the interaction between a free fluid and a poroelastic plate. The bulk flow is governed by the Stokes Equation, while the surface dynamics are described by the Biot–Kirchhoff Poroelastic Plate. We discuss the main ideas in analyzing the model and highlight its applicability.