Sanghyun Lee
Associate Professor
Department of Mathematics
Florida State University (FSU)

"Physics Preserving Finite Element Methods for Coupled Multi-Physical Applications"

Sep 27, 2023

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Abstract:

In this talk, we will discuss new finite element methods for solving three distinct problems: coupled flow and transport systems in porous media, linear elasticity (mechanics) equations, and the coupled mechanics and flow, known as poroelasticity. The primary goal of this study is to develop computationally efficient and robust numerical methods that are free from both oscillations due to the lack of local conservation and locking effects.

The locally conservative enriched Galerkin (LF-EG) method, which will be used to solve the flow problem, is constructed by adding a constant function to each element based on classical continuous Galerkin methods. The locking-free enriched Galerkin (LC-EG) method adds a vector to the displacement space. These EG methods employ well-known discontinuous Galerkin (DG) techniques, but the approximation spaces have fewer degrees of freedom compared to typical DG methods, thus offering an efficient alternative to DG methods. We will present a priori error estimates of optimal order and demonstrate, through numerical examples, that the new method is free from oscillations and locking.