多边形网格
稳健性(进化)
数学
多项式次数
应用数学
Curl(编程语言)
多项式的
减刑
计算机科学
算法
数学分析
几何学
物理
量子力学
生物化学
基因
电压
化学
程序设计语言
作者
L. Beirão da Veiga,Franco Dassi,Daniele Antonio Di Pietro,Jérôme Droniou
标识
DOI:10.1016/j.cma.2022.115061
摘要
This paper contains two major contributions. First we derive, following the discrete de Rham (DDR) and Virtual Element (VEM) paradigms, pressure-robust methods for the Stokes equations that support arbitrary orders and polyhedral meshes. Unlike other methods presented in the literature, pressure-robustness is achieved here without resorting to an H(div)-conforming construction on a submesh, but rather projecting the volumetric force onto the discrete H(curl) space. The cancellation of the pressure error contribution stems from key commutation properties of the underlying DDR and VEM complexes. The pressure-robust error estimates in hk+1 (with h denoting the meshsize and k≥0 the polynomial degree of the DDR or VEM complex) are proven theoretically and supported by a panel of three-dimensional numerical tests. The second major contribution of the paper is an in-depth study of the relations between the DDR and VEM approaches. We show, in particular, that a complex developed following one paradigm admits a reformulation in the other, and that couples of related DDR and VEM complexes satisfy commuting diagram properties with the degrees of freedom maps.
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