This is a past event.

Please join the Department of Mathematical Sciences in Fisher Hall 326 on Thursday, April 9 from 12:00 - 1:00 p.m. for our Graduate Student Seminar Series. 

Refreshments will be provided.

Contact the Math Department Graduate Program Assistant, Andi Schoch, via email (ajschoch@mtu.edu) or in person (Fisher Hall 318) with any questions. 

Presenting this week is Qiuyun Jin and Caleb Hiltunen.

Qiuyun will be presenting on Stability and error estimates of local discontinuous Galerkin methods for incompressible miscible displacements with Darcy-Forchheimer model.
Abstract: The miscible displacement problem in porous media, governed by the Darcy–Forchheimer model, describes the flow and transport of miscible fluids and arises in a range of applications including groundwater contamination and enhanced oil recovery. The governing system couples a convection-diffusion equation for the concentration with a nonlinear elliptic system for the pressure and velocity , and the strong nonlinear coupling inherent in this formulation gives rise to substantial analytical difficulties. A local discontinuous Galerkin (LDG) discretization is employed for the two-dimensional incompressible problem, and a rigorous numerical analysis of the resulting semi-discrete scheme is carried out. 
Stability is established separately for the transport variables and the flow variables, via a discrete energy argument and the inf-sup condition, respectively. To handle the nonlinear Darcy–Forchheimer term, a cut-off technique is introduced for the velocity field, and a modified coefficient is employed to facilitate the treatment of the resulting nonlinear terms in the analysis. Moreover, optimal error estimates are derived for both the concentration and the velocity . The analysis makes essential use of specially designed projection operators whose compatibility with the alternating numerical fluxes guarantees the cancellation of inter-element jump terms, together with a priori bounds on the numerical solution that permit a rigorous treatment of the nonlinear terms. Numerical experiments are presented to validate the theoretical convergence results.

Caleb will present Improving the Power of Bonferroni Adjustments under Joint Normality and Exchangeability.
Abstract: Bonferroni’s correction is a popular tool to address multiplicity but is notorious for its low power when tests are dependent. We propose a practical modification of Bonferroni’s correction when test statistics are jointly normal and exchangeable. This method is applicable for practitioners and achieves higher power in sparse alternatives as suggested by simulations. We show that this method successfully controls the family-wise error rate at any significance level.