A MIXED FINITE ELEMENT AND CHARACTERISTIC MIXED FINITE ELEMENT FOR INCOMPRESSIBLE MISCIBLE DARCY-FORCHHEIMER DISPLACEMENT AND NUMERICAL ANALYSIS  

作　　者：袁益让 李长峰 孙同军 杨青 Yirang YUAN;Changfeng LI;Tongjun SUN;Qing YANG(Institute of Mathematics,Shandong University,Jinan 250100,China;School of Economics,Shandong University,Jinan 250100,China;School of Mathematical Sciences,Shandong Normal University,Jinan 250014,China)

机构地区：[1]Institute of Mathematics,Shandong University,Jinan 250100,China [2]School of Economics,Shandong University,Jinan 250100,China [3]School of Mathematical Sciences,Shandong Normal University,Jinan 250014,China

出　　处：《Acta Mathematica Scientia》2023年第5期2026-2042,共17页数学物理学报（B辑英文版）

基　　金：supported by the Natural ScienceFoundation of Shandong Province(ZR2021MA019)。

摘　　要：In this paper a mixed finite element-characteristic mixed finite element method is discussed to simulate an incompressible miscible Darcy-Forchheimer problem.The flow equation is solved by a mixed finite element and the approximation accuracy of Darch-Forchheimer velocity is improved one order.The concentration equation is solved by the method of mixed finite element,where the convection is discretized along the characteristic direction and the diffusion is discretized by the zero-order mixed finite element method.The characteristics can confirm strong stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation.In actual computations the characteristics adopts a large time step without any loss of accuracy.The scalar unknowns and its adjoint vector function are obtained simultaneously and the law of mass conservation holds in every element by the zero-order mixed finite element discretization of diffusion flux.In order to derive the optimal 3/2-order error estimate in L^(2) norm,a post-processing technique is included in the approximation to the scalar unknowns.Numerical experiments are illustrated finally to validate theoretical analysis and efficiency.This method can be used to solve such an important problem.

关 键 词：Darcy-Forchheimer miscible displacement mixed element-characteristic mixed element-postprocessing scheme local conservation of mass 3/2-order error estimates in L^(2)-norm numerical computation 

分 类 号：O241.82[理学—计算数学]