Error analysis of a mixed finite element method for a Cahn–Hilliard–Hele–Shaw system

• Published in: Numerische Mathematik Vol. 135; no. 3; pp. 679 - 709
• Main Authors: Liu, Yuan, Chen, Wenbin, Wang, Cheng, Wise, Steven M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2017; Springer Nature B.V
• Subjects: Chemical potential; Convergence; Error analysis; Error functions; Finite element method; Mathematical analysis; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Nonlinear analysis; Numerical Analysis; Numerical and Computational Physics; Simulation; Spatial resolution; Theoretical; 65K10; 65M60; 35K35; 65M12; 35K55

We present and analyze a mixed finite element numerical scheme for the Cahn–Hilliard–Hele–Shaw equation, a modified Cahn–Hilliard equation coupled with the Darcy flow law. This numerical scheme was first reported in Feng and Wise (SIAM J Numer Anal 50:1320–1343, 2012 ), with the weak convergence to...