A combined discontinuous Galerkin finite element method for miscible displacement problem

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• 作者：Jiansong Zhang^a ; ^{jszhang@upc.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Jiang Zhu^b ; ^{jiang@lncc.br" class="auth_mail" title="E-mail the corresponding author} ; Rongpei Zhang^c ; ^{rpzhang@lncc.br" class="auth_mail" title="E-mail the corresponding author} ; Danping Yang^d ; ^{dpyang@math.ecnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Abimael F.D. Loula^b ; ^{aloc@lncc.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65M30 ; 65M15
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：44-55
• 全文大小：1956 K

文摘

A new combined method is constructed for solving incompressible miscible displacement in porous media. In this procedure, a hybrid mixed element method is constructed for the pressure and velocity equation, while a symmetric discontinuous Galerkin finite element method is proposed for the concentration equation. The introduction of these two numerical methods not only makes the coefficient matrixes symmetric positive definite, but also conserves the local mass balance. The stability and consistency of the method are analyzed and the optimal error estimate in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S037704271630293X&_mathId=si15.gif&_user=111111111&_pii=S037704271630293X&_rdoc=1&_issn=03770427&md5=0cea8aec438f18a01c024ddfb71ea7ea" title="Click to view the MathML source">L^∞(L²)class="mathContainer hidden">class="mathCode">$L^{\infty }\left(L^2\right)$ for velocity and concentration and the super convergence in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S037704271630293X&_mathId=si16.gif&_user=111111111&_pii=S037704271630293X&_rdoc=1&_issn=03770427&md5=b41825126b431ae23f783464bbe32087" title="Click to view the MathML source">L^∞(H¹)class="mathContainer hidden">class="mathCode">$L^{\infty }\left(H^1\right)$ for pressure are derived. Finally, some numerical results are presented.