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.

中文翻译：

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四阶非线性问题的连续/不连续伽辽金近似

我们引入了具有内部惩罚项的连续/不连续 Galerkin 有限元方法 (CDFEM) 来解决非线性四阶问题，该问题出现在分析 Stokes 系统控制的流体流动的限制中。对于相关的连续和离散问题，我们证明了弱解的存在性和唯一性。分析显示了该方法的一致性、稳定性和收敛性。为了显示数值模型的适用性和稳健性，执行了几个测试用例。