p-Laplace问题的混合高阶方法  

THE HYBRID HIGH-ORDER METHOD FOR p-LAPLACE PROBLEM

作　　者：任云云 刘东杰[1] Ren Yunyun;Liu Dongjie(Department of Mathematics,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学数学系,上海200444

出　　处：《计算数学》2024年第4期397-408,共12页Mathematica Numerica Sinica

摘　　要：本文主要考虑1<p<∞时p-Laplace问题的混合高阶方法(HHO方法).即利用最高次数大于1的分段多项式函数逼近离散未知数,数值变量在Raviart-Thomas有限元空间中进行局部梯度重构,用高阶梯度Ru_(h)代替传统梯度D_(v),且其无需在正则三角剖分上稳定.我们从能量的角度出发,将离散能量极小值进行梯度重构,在新的距离框架下,通过引入离散应力,得到了HHO方法的先验和后验误差估计.数值算例验证了该混合高阶方法的可靠性和有效性.The article consider hybrid high-order methods(HHO)for the p-Laplace problem when 1<p<∞.The approximation by HHO methods utilizes a reconstruction of the gradients with piecewise Raviart-Thomas finite elements on a regular triangulation without stabilization.Using high-order gradient Ru_(h)for local gradient reconstruction in piecewise Raviart Thomas finite element space instead of gradient D_(v).From the perspective of energy,we perform gradient reconstruction on the minimum value of discrete energy,and determine the discrete stress in a new framework of distance.The main results are the a priori and a posteriori error estimates with global upper bound and global lower bound.Numerical benchmarks display higher convergence rates for the HHO method.

关 键 词：p-Laplace问题 混合高阶方法 先验误差估计 后验误差估计 

分 类 号：O241.82[理学—计算数学]