Department of Mathematics and Statistics Colloquium (Apr 10)
When: April 10, 2025
Location: IES 110
Time: 4:00 - 5:00pm (Light refreshment will be served on the 5th floor of BVM at 3:30pm)
Speaker: Dr. Natasha S. Sharma (University of Texas, El Paso)
Topic: Sixth order phase field models capturing microstructure evolution and microemulsions
Description: Sixth order phase field models have emerged as a relatively new modeling technique that effectively captures important physical processes such as microstructure evolution and microemulsions. These processes find applications in material science, physics, drug delivery design systems and enhanced oil recovery. Mathematically, these models belong to a class of nonlinear parabolic equations involving sixth-order spatial derivatives. The higher order spatial derivatives appearing in the equations combined with a highly stiff time dependent process present many challenges to design a stable, convergent and efficient numerical method approximating solutions to these equations. In this talk we will discuss two numerical methods based on a finite element method to overcome the challenges. The performance of our proposed methods will be demonstrated through the results of some numerical experiments illustrating the ability of our methods to capture the two physical processes accurately.
When: April 10, 2025
Location: IES 110
Time: 4:00 - 5:00pm (Light refreshment will be served on the 5th floor of BVM at 3:30pm)
Speaker: Dr. Natasha S. Sharma (University of Texas, El Paso)
Topic: Sixth order phase field models capturing microstructure evolution and microemulsions
Description: Sixth order phase field models have emerged as a relatively new modeling technique that effectively captures important physical processes such as microstructure evolution and microemulsions. These processes find applications in material science, physics, drug delivery design systems and enhanced oil recovery. Mathematically, these models belong to a class of nonlinear parabolic equations involving sixth-order spatial derivatives. The higher order spatial derivatives appearing in the equations combined with a highly stiff time dependent process present many challenges to design a stable, convergent and efficient numerical method approximating solutions to these equations. In this talk we will discuss two numerical methods based on a finite element method to overcome the challenges. The performance of our proposed methods will be demonstrated through the results of some numerical experiments illustrating the ability of our methods to capture the two physical processes accurately.