Continuous/discontinuous Galerkin approximations for a fourth-order nonlinear problem

Computers and Mathematics with Application, 97 (2021), 122-152
http://doi.org/10.1016/j.camwa.2021.05.034

We introduce a Continuous/Discontinuous Galerkin Finite Element Method (CDFEM) with interior penalty terms to solve a nonlinear fourth-order problem that appears in the analysis of the confinement of fluid flows governed by the Stokes system. For the associated continuous and discrete problems, we prove the existence and uniqueness of weak solutions. Consistency, stability and convergence of the method are shown analytically. To show the applicability and robustness of the numerical model, several test cases are performed.