CAM Seminar

Computational and Applied Mathematics Seminar

Spring 2021

Mondays at 4:10 p.m. via ZOOM talks

(Note the starting time maybe a few minutes later following the adjusted class times on MWF required by the University)

The CAM Seminar is organized in the ISU Mathematics Department. It brings speakers from inside and outside of ISU, raising issues and exchanging ideas on topics of current interest in the are of computational and applied mathematics.

  • February 22

       Title:  A $C^0$ finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain

       Peimeng Yin

       Wayne State University 

Abstract: In our work, we study the biharmonic equation with the Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-order problem into a system of Poisson equations. Different from the usual mixed method that leads to two Poisson problems but only applies to convex domains, the proposed decomposition involves a third Poisson equation to confine the solution in the correct function space, and therefore can be used in both convex and non-convex domains. A $C^0$ finite element algorithm is in turn proposed to solve the resulted system. In addition, we derive the optimal error estimates for the numerical solution on both quasi-uniform meshes and graded meshes. Numerical test results are presented to justify the theoretical findings. This is a joint work with Hengguang Li and Zhimin Zhang.

ZOOM Link:

Join from a PC, Mac, iPad, iPhone or Android device:

    Please click this URL to start or join. https://iastate.zoom.us/j/99184686787
    Or, go to https://iastate.zoom.us/join and enter meeting ID: 991 8468 6787  
 
Join from dial-in phone line:

    Dial: +1 646 876 9923 or +1 301 715 8592
    Meeting ID: 991 8468 6787
    Participant ID: Shown after joining the meeting
    International numbers available: https://iastate.zoom.us/u/abn9qT9Vc6

 

  • March 01

       Title:  Nonlocality in nonlinear conservation model

       Anh Thuong Vo

       University of Nebraska-Lincoln

Abstract:  In this talk, we investigate the convergence of solutions of nonlocal conservation PDE to the local counterparts in one space dimension. Nonlocal operators are integral operators that mimic differential operators but account for long-range interactions over a finite horizon. Nonlocality appears in many physical phenomena (fracture, phase separation) and has a wide range of applications (image processing). In Du et al, it was shown that nonlocal operators can be reduced into local operators in a distributional sense. The solution of the nonlocal Burgers equation is also shown to converge to the local counterpart numerically. In our research, we generalize the nonlocal advection operator. In the limit when the horizon parameter approaches zero, we are able to prove nonlocal operator convergence pointwise to its local counterpart. Then, we apply the result to show the convergence of the solution of the nonlocal conservation equation to the local counterpart.

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  • March 08

       Title: 

       Xinfeng Liu

       University 

Abstract: 

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  • March 15

       Title: 

       Zhongming Wang

       University 

Abstract: 

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  • March 22

       Title: 

       Shuwang Li

       University 

Abstract: 

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  • March 29

       Title: 

       Rongjie Lai

       University 

Abstract: 

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  • April 05

       Title: 

       Robert Basili

       Iowa State University 

Abstract: 

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  • April 12

       Title: 

       Wei Zhu

       University 

Abstract: 

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  • April 19

       Title: 

       Junshan Lin

       Auburn University 

Abstract: 

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  • April 26

       Title: 

       Speaker

       University 

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  • February 01

       Title: 

       Speaker

       University 

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  • February 08

       Title:  Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential

       Cheng Wang

       University of Massachusetts Dartmouth

Abstract: 

The Cahn-Hilliard model with logarithmic potential is considered, in which the key difficulty has always been associated with the singularity of the logarithmic terms. An energy stable finite difference scheme, which implicitly treats the logarithmic terms, is proposed and analyzed in this talk. In particular, how to ensure the positivity of the logarithmic arguments, so that the numerical scheme is well-defined at a point-wise level, has been a long-standing mathematical challenge. It is proved that, given any numerical solution with a fixed bound at the previous time step, there exists a unique numerical solution that satisfies the given bound (-1,1) at a point-wise level. As a result, the numerical scheme is proven to be well-defined, and the unique solvability and energy stability could be established with the help of convexity analysis. In addition, an optimal rate convergence analysis could be appropriately established. Some numerical results are also presented in the talk.

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  • February 15

       Title: 

       Speaker

       University 

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