<?xml version="1.1" encoding="utf-8"?>
<article xsi:noNamespaceSchemaLocation="http://jats.nlm.nih.gov/publishing/1.1/xsd/JATS-journalpublishing1-mathml3.xsd" dtd-version="1.1" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><front><journal-meta><journal-id journal-id-type="publisher-id">EST</journal-id><journal-title-group><journal-title>Educational Science Theory</journal-title></journal-title-group><issn>2995-4835</issn><eissn>2995-4843</eissn><publisher><publisher-name>Art and Technology</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.61369/EST.20240800011</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title>Cahn-Hillard 方程的虚拟元方法</title><url>https://artdesignp.com/journal/EST/2/8/10.61369/EST.20240800011</url><author>周莹莹</author><pub-date pub-type="publication-year"><year>2024</year></pub-date><volume>2</volume><issue>8</issue><history><date date-type="pub"><published-time>2024-08-20</published-time></date></history><abstract>本文提出使用C0连续的非协调虚拟元方法求解二维的Cahn-Hillard 方程. 该虚拟元方法降低了经典虚拟元方法对连续性的要求. 本文利用自由度生成三种投影算子，再利用投影算子建立半离散格式，最后对生成的半离散格式进行误差估计。</abstract><keywords>虚拟元方法,Cahn-Hillard 方程,误差估计</keywords></article-meta></front><body/><back><ref-list><ref id="B1" content-type="article"><label>1</label><element-citation publication-type="journal"><p>[1]DEDNER A, HODSON A. A higher order nonconforming virtual element method for the Cahn-Hilliard equation[J]. Journal of Scientific Computing, 2024, 101: 81.[2] 郭靖.Cahn-Hilliard 方程的高精度快速算法及其应用研究[D]. 华南理工大学,2024.[3]Antonietti, P. F., et al.,AC1virtual element method for the Cahn-Hilliard equation with polygonal meshes.&amp;rdquo; SIAM Journal on Numerical Analysis, 54(1), 34-57(2016).[4]Deng, Q., &amp;amp; Wei, H.,Deng, Q., &amp;amp; Wei, H. A C&amp;sup1; virtual element method for the Cahn&amp;ndash;Hilliard equation on polygonal meshes. SIAM Journal on Numerical Analysis,55(2), 547-574(2017).[5]Antonietti, P. F., et al. A mixed virtual element method for the Cahn-Hilliard equation.Mathematical Models and Methods in Applied Sciences, 28(09), 1743-1785(2018).[6]Han, D., &amp;amp; Wang, X. A mixed virtual element method for the dynamical Cahn&amp;ndash;Hilliard equation. Journal of Computational Physics, 419, 109398 (2020).[7]Zhang, J., &amp;amp; Yang, X. An adaptive virtual element method for the Cahn-Hilliard equation. Computer Methods in Applied Mechanics and Engineering, 367, 113101(2020).[8]Li, Y.,Chen, L. A second-order energy stable scheme for the Cahn-Hilliard equation using the virtual element method. Applied Numerical Mathematics, 169, 265-281(2021).[9]Wu, S., &amp;amp; Li, M., A virtual element method for the coupled Cahn-Hilliard&amp;ndash;Navier&amp;ndash;Stokes system. Computer Methods in Applied Mechanics and Engineering, 377,113687(2022).[10]Liu, H., Gao, F., A virtual element method for the anisotropic Cahn&amp;ndash;Hilliard equation. Journal of Scientific Computing, 90(1), 13 (2022).[11]Wang, K., &amp;amp; He, X., Efficient solver and preconditioning techniques for the virtual element discretization of the Cahn-Hilliard equation. Journal of Computational Physics,491, 112375. (2023).[12]Zhang, B., Zhao, J., &amp;amp; Chen, S. (2020). The nonconforming virtual element method for fourth-order singular perturbation problem. Advances in Computational Mathematics, 46(1), 19.[13]Brenner, S.C., Scott, L.R.: The mathematical theory of finite element methods. No. 15 in Texts in applied mathematics, 3rd edn. Springer, New York (2008).[14]Beir&amp;atilde;oda Veiga, L., Brezzi, F., Cangiani, A., Manzini, G., Marini, L.D., Russo, A.: Basic principles of virtual element methods. Math. Models Methods Appl. Sci. 23(01), 199-214 (2013).[15]Elliott, C.M., French, D.A.: A nonconforming finite-element method for the two-dimensional Cahn-Hilliard equation.SIAMJ.Numer.Anal.26(4),884-903(1989).[16]Dedner, A., Hodson, A.: Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients. IMA J. Numer. Anal. 42(2), 1364-1399 (2022).</p><pub-id pub-id-type="doi"/></element-citation></ref></ref-list></back></article>
