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Partial Differential Equations & Applied Math: "Direct discontinuous Galerkin methods for Keller-Segel Chemotaxis equations "

Dr. Jue Yan, Iowa State University

Wednesday, March 8, 2017
  1:10–2 p.m.

Location: Surge Building 268
  Parking Information

Category: Seminar

Description: We develop direct discontinuous Galerkin (DDG) methods to solve Keller-Segel Chemotaxis equations. Different to available DG methods or other numerical methods in literature, we introduce no extra variable to approximate the chemical density gradients and solve the system directly. With P^k polynomial approximations, we observe no order loss and optimal (k 1)th order convergence is obtained. The reason that DDG methods have better convergence is because that DDG methods have super convergence phenomena on approximating solution gradients. With Fourier (Von Neumann) analysis technique, we prove the DDG solution’s spatial derivative is super convergent with at least (k 1)th order under momentum norm or in weak sense.  We show the cell density approximations are strictly positive with at least third order of accuracy. Blow up features are captured well.

Additional Information: Math Seminars

Open to: General Public
Admission: Free
Sponsor: Mathematics

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