High order finite difference WENO methods with unequal-sized sub-stencils for the DP type equations

主讲人：仲杏慧 浙江大学教授

时间：2022年5月31日10：00

地点：腾讯会议 482 114 740

举办单位：数理学院

主讲人介绍：仲杏慧，2007年获中国科学技术大学学士学位，2012年获美国布朗大学博士学位。随后在密歇根州立大学和犹他大学从事博士后研究工作。现任浙江大学百人计划研究员、博士生导师。研究方向为数值分析，科学计算，不确定性量化等领域，主要研究工作包括间断有限元方法的算法设计及其分析、动力学传输方程的数值模拟及其在等离子体物理中的应用、不确定量化及随机计算算法及应用等方面。

内容介绍：In this talk, we present finite difference weighted essentially non-oscillatory (WENO) schemes with unequal-sized sub-stencils for solving the Degasperis-Procesi (DP) and μ- Degasperis-Procesi (μDP) equations, which contain nonlinear high order derivatives, and possibly peakon solutions or shock waves. By introducing auxiliary variable(s), we rewrite the DP equation as a hyperbolic-elliptic system, and the μDP equation as a first order system. Then we choose a linear finite difference scheme with suitable order of accuracy for the auxiliary variable(s), and finite difference WENO schemes with unequal-sized sub-stencils for the primal variable. Comparing with the classical WENO scheme which uses several small stencils of the same size to make up a big stencil, WENO schemes with unequal-sized sub-stencils are simple in the choice of the stencil and enjoy the freedom of arbitrary positive linear weights. Another advantage is that the final reconstructed polynomial on the target cell is a polynomial of the same degree as the polynomial over the big stencil, while the classical finite difference WENO reconstruction can only be obtained for specific points inside the target interval. Numerical tests are provided to demonstrate the high order accuracy and non-oscillatory properties of the proposed schemes.