Sobolev方程的高阶有限元法研究  

Research of High-order Finite Element Method for Sobolev Equation

作　　者：谢春梅[1] XIE Chunmei(Chengdu Aeronautic Polytechnic,Chengdu 610100,China)

机构地区：[1]成都航空职业技术学院,成都610100

出　　处：《成都航空职业技术学院学报》2023年第2期44-47,共4页Journal of Chengdu Aeronautic Polytechnic

摘　　要：针对带有对流项的Sobolev方程,结合高阶杂交有限元方法与投影稳定化技巧,提出半离散格式的高阶有限元方法。离散解由单元内部与单元边界两部分组成,分别采用等阶多项式空间来逼近。经过梯度及对流项重构并增加合适的稳定项后,此方法具有三个特点:(1)具有稳定性;(2)具有高阶误差估计;(3)在对流占优情况下误差估计也成立。For the Sobolev equation with convection term,a semi-discrete format of high-order finite element method is proposed by combining hybrid high-order finite element method and projection stabilization.The discrete solution consists of two parts:the interior and the boundary of each element,which are approximated by using equal order polynomial spaces respectively.After the gradient and convection terms are reconstructed and a suitable stability term is added,this method has three characteristics:(1)stability;(2)high-order error estimation;(3)the error estimate is also valid for the convection-dominated case.

关 键 词：SOBOLEV方程 对流项 高阶有限元法 

分 类 号：O242[理学—计算数学]