Mixed Schemes for Fourth-Order DIV Equations

Author:

Fan Ronghong1,Liu Yanru2,Zhang Shuo1

Affiliation:

1. LSEC , Institute of Computational Mathematics and Scientific/Engineering Computing , Academy of Mathematics and System Sciences , Chinese Academy of Sciences , Beijing 100190 , P. R. China

2. School of Mathematical Sciences , Peking University , Beijing 100871 , P. R. China

Abstract

Abstract In this paper, stable mixed formulations are designed and analyzed for the quad div problems under two frameworks presented in [23] and [22], respectively. Analogue discretizations are given with respect to the mixed formulation, and optimal convergence rates are observed, which confirm the theoretical analysis.

Funder

National Natural Science Foundation of China

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

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3. S. C. Brenner, J. Sun and L.-Y. Sung, Hodge decomposition methods for a quad-curl problem on planar domains, J. Sci. Comput. 73 (2017), no. 2–3, 495–513.

4. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, Stud. Math. Appl. 4, North-Holland Publishing, Amsterdam, 1978.

5. P. G. Ciarlet and P. Raviart, A mixed finite element method for the biharmonic equation, Mathematical Aspects of Finite Elements in Partial Differential Equations, Academic Press, New York (1974), 125–145.

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Three families of grad div-conforming finite elements;Numerische Mathematik;2022-10-11

2. DPG Methods for a Fourth-Order div Problem;Computational Methods in Applied Mathematics;2022-05-24

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