The Bulk-Surface Virtual Element Method for Reaction-Diffusion PDEs:Analysis and Applications

作     者：Massimo Frittelli Anotida Madzvamuse Ivonne Sgura 

作者机构：Department of Mathematics and Physics“E.De Giorgi”University of SalentoVia per Arnesano73100 LecceItaly Department of MathematicsUniversity of British Columbia1984 Mathematics RoadVancouverBC V6T 1Z2Canada Department of MathematicsSchool of Mathematical and Physical SciencesUniversity of SussexBrightonBN19QHUK Department of Mathematics and Applied MathematicsUniversity of PretoriaPrivate Bag x 20Hatfield0028South Africa. 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2023年第33卷第3期

页      面：733-763页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：Regione Puglia(Italy)through the research programme REFIN-Research for Innovation(protocol code 901D2CAA,project No.UNISAL026) MF acknowledges support from the Italian National Institute of High Mathematics(INdAM)through the INdAM-GNCS Project no.CUP E55F22000270001 the Global Challenges Research Fund through the Engineering and Physical Sciences Research Council grant number EP/T00410X/1:UK-Africa Postgraduate Advanced Study Institute in Mathematical Sciences,the Health Foundation(1902431) the NIHR(NIHR133761)and by the Discovery Grant awarded by Canadian Natural Sciences and Engineering Research Council(2023-2028) AM acknowledges support from the Royal Society Wolfson Research Merit Award funded generously by the Wolfson Foundation(2016-2021) AM is a Distinguished Visiting Scholar to the Department of Mathematics,University of Johannesburg,South Africa,and the University of Pretoria in South Africa.IS and MF are members of the INdAM-GNCS activity group.The work of IS is supported by the PRIN 2020 research project(no.2020F3NCPX)”Mathematics for Industry 4.0”,and from the”National Centre for High Performance Computing,Big Data and Quantum Computing”funded by European Union-NextGenerationEU,PNRR project code CN00000013,CUP F83C22000740001 

主　　题：Bulk-surface PDEs bulk-surface reaction-diffusion systems polyhedral meshes bulksurface virtual element method convergence. 

摘      要：Bulk-surface partial differential equations(BS-PDEs)are prevalent in manyapplications such as cellular,developmental and plant biology as well as in engineeringand material *** numerical methods for BS-PDEs in three space dimensions(3D)are *** this work,we present a bulk-surface virtual elementmethod(BS-VEM)for bulk-surface reaction-diffusion systems,a form of semilinearparabolic BS-PDEs in *** previous studies in two space dimensions(2D),the3D bulk is approximated with general polyhedra,whose outer faces constitute a flatpolygonal approximation of the *** this reason,the method is restricted tothe lowest order case where the geometric error is not *** BS-VEM guaranteesall the advantages of polyhedral methods such as easy mesh generation andfast matrix assembly on general *** advantages are much more relevantthan in *** allowing for general polyhedra,general nonlinear reaction kineticsand general surface curvature,the method only relies on nodal values without needingadditional evaluations usually associated with the quadrature of general *** latter is particularly costly in *** BS-VEM as implemented in thisstudy retains optimal convergence of second order in space.