finite element method

Theory and Implementation of Novel Numerical Methods for Multiphysics Interface Problems

Najwa Alshehri, Ph.D. Student, Applied Mathematics and Computational Sciences

Jul 8, 15:00 - 17:00

B2/B3 L0 R0215

finite element method numerical analysis fluid-structure interactions mixed finite elements

This thesis develops and analyzes Finite Element Methods (FEM) for multiphysics interface problems using the Fictitious Domain with Distributed Lagrange Multiplier (FD-DLM) framework. It introduces new families of stable mixed methods with discontinuous Lagrange multiplier spaces, studies both a priori and a posteriori error estimates, and designs multigrid preconditioners. Theoretical results are supported by numerical experiments.