Monotonicity Correction for the Finite Element Method of Anisotropic Diffusion Problems  

作　　者：Boyang Yu Hongtao Yang Yonghai Li Guangwei Yuan 

机构地区：[1]School of Mathematics,Jilin University,Changchun 130012,China [2]Institute of Applied Physics and Computational Mathematics,Fenghaodong Road,Haidian District,Beijing 100094,China

出　　处：《Communications in Computational Physics》2022年第5期1489-1524,共36页计算物理通讯（英文）

基　　金：supported by the Science Challenge Project(No.TZ2016002);the National Science Foundation of China(No.12071177,No.11971069).

摘　　要：We apply the monotonicity correction to thefinite element method for the anisotropic diffusion problems,including linear and quadraticfinite elements on triangular meshes.When formulating thefinite element schemes,we need to calculate the integrals on every triangular element,whose results are the linear combination of the two-point pairs.Then we decompose the integral results into the main and remaining parts according to coefficient signs of two-point pairs.We apply the nonlinear correction to the positive remaining parts and move the negative remaining parts to the right side of thefinite element equations.Finally,the original stiffness matrix can be transformed into a nonlinear M-matrix,and the corrected schemes have the positivity-preserving property.We also give the monotonicity correction to the time derivative term for the time-dependent problems.Numerical experiments show that the correctedfinite element method has monotonicity and maintains the convergence order of the original schemes in H1-norm and L2-norm,respectively.

关 键 词：Thefinite element method nonlinear M-matrix monotonicity correction positivity-preserving property two-point pair 

分 类 号：O17[理学—数学]