Speaker: Dr. Zheng Sun, Assistant Professor, University of Alabama (zsun30@ua.edu)
Date: Friday, October 18, 2024, 4:15 – 5:15 PM
Location: Science Engineering Hall (SCEN 404) in-person.
If you wish to receive the Zoom link, please contact Dr. Chen Liu
Title: OEDG: Oscillation-Eliminating Discontinuous Galerkin Method for Hyperbolic Conserva- tion Laws
Abstract: Controlling spurious oscillations is crucial for designing reliable numerical schemes for hyperbolic conservation laws. In this talk, we propose a novel, robust, and efficient oscillation- eliminating discontinuous Galerkin (OEDG) method on general meshes, motivated by the damping technique in [Lu, Liu, and Shu, SIAM J. Numer. Anal., 59:1299–1324, 2021]. The OEDG method incorporates an OE procedure after each Runge–Kutta stage, and it is devised by alternately evolv- ing the conventional semidiscrete DG scheme and a damping equation. A novel damping operator is designed to possess both scale-invariant and evolution-invariant properties. We rigorously prove optimal error estimates of the fully discrete OEDG method for smooth solutions of linear scalar conservation laws. The OEDG method exhibits many notable advantages. It effectively eliminates spurious oscillations for problems spanning various scales and wave speeds without problem-specific parameters. Furthermore, it retains the key properties of the conventional DG method, such as conservation, optimal convergence rates, and superconvergence. Moreover, the OEDG method maintains stability under the normal CFL condition, even in the presence of strong shocks asso- ciated with highly stiff damping terms. The OE procedure is non-intrusive, facilitating seamless integration into existing DG codes as an independent module. Extensive numerical results confirm the analysis and validate the effectiveness of the OEDG method.
Short Bio: Dr. Zheng Sun is an Assistant Professor in the Department of Mathematics at the Uni- versity of Alabama. His research specializes in numerical methods for partial differential equations, with a particular emphasis on Discontinuous Galerkin finite element methods, time discretization techniques, structure-preserving methods for physical and biological models, and numerical ap- proaches for kinetic models and hyperbolic problems. Prior to his appointment at the University of Alabama, Dr. Sun served as a Visiting Assistant Professor in the Department of Mathematics at Ohio State University. He earned his Ph.D. in Applied Mathematics from Brown University.
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