典型文献
Superconvergent Interpolatory HDG Methods for Reaction Diffusion Equations Ⅱ:HHO-Inspired Methods
文献摘要：
In Chen et al.(J.Sci.Comput.81(3):2188-2212,2019),we considered a superconver-gent hybridizable discontinuous Galerkin(HDG)method,defined on simplicial meshes,for scalar reaction-diffusion equations and showed how to define an interpolatory version which maintained its convergence properties.The interpolatory approach uses a locally postprocessed approximate solution to evaluate the nonlinear term,and assembles all HDG matrices once before the time integration leading to a reduction in computational cost.The resulting method displays a superconvergent rate for the solution for polynomial degree k≥1.In this work,we take advantage of the link found between the HDG and the hybrid high-order(HHO)methods,in Cockburn et al.(ESAIM Math.Model.Numer.Anal.50(3):635-650,2016)and extend this idea to the new,HHO-inspired HDG methods,defined on meshes made of general polyhedral elements,uncovered therein.For meshes made of shape-regular polyhedral elements affine-equivalent to a finite number of reference ele-ments,we prove that the resulting interpolatory HDG methods converge at the same rate as for the linear elliptic problems.Hence,we obtain superconvergent methods for k≥0 by some methods.We thus maintain the superconvergence properties of the original methods.We present numerical results to illustrate the convergence theory.
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作者姓名：
Gang Chen;Bernardo Cockburn;John R.Singler;Yangwen Zhang
作者机构：
College of Mathematics,Sichuan University,Chengdu 610065,Sichuan,China;School of Mathematics,University of Minnesota,Minneapolis,MN,USA;Department of Mathematics and Statistics,Missouri University of Science and Technology,Rolla,MO,USA;Department of Mathematical Science,University of Delaware,Newark,DE,USA
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引用格式：
[1]Gang Chen;Bernardo Cockburn;John R.Singler;Yangwen Zhang-.Superconvergent Interpolatory HDG Methods for Reaction Diffusion Equations Ⅱ:HHO-Inspired Methods)[J].应用数学与计算数学学报,2022(02):477-499
A类：
Superconvergent,Interpolatory,Comput,superconver,hybridizable,simplicial,interpolatory,postprocessed,superconvergent,Cockburn,ESAIM
B类：
HDG,Methods,Reaction,Diffusion,Equations,HHO,Inspired,Chen,Sci,considered,discontinuous,Galerkin,defined,meshes,scalar,reaction,diffusion,equations,showed,version,which,maintained,its,properties,approach,uses,locally,approximate,solution,evaluate,nonlinear,term,assembles,matrices,once,before,integration,leading,reduction,computational,cost,resulting,displays,polynomial,degree,this,work,take,advantage,link,found,between,high,order,methods,Math,Model,Numer,Anal,extend,idea,new,inspired,made,general,polyhedral,elements,uncovered,therein,For,shape,regular,affine,equivalent,finite,number,reference,prove,that,same,elliptic,problems,Hence,obtain,by,some,We,thus,superconvergence,original,present,numerical,results,illustrate,theory
AB值：
0.488092
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