Error Analysis for a Nonconforming Finite Element Discretization of the 3D-CCPF Model

This paper presents an a-priori and a-posteriori error analysis for the time-dependent case of a coupled continuum pipe-fow in three dimensions on anisotropic meshes (i.e. elements with very large aspect ratio). Our investigation includes nonconforming discretizations as well as different elements and different versions of Crouzeix-Raviart fnite element methods. Under suitable regularity assumptions on the exact solution, we derive optimal a priori error estimates in the H^1-like norm. Leveraging residual elements, local error indicators and a global estimator are generated, demonstrating reliability and efficiency. The efficiency of error estimators holds unconditional, though its reliability involves the alignment measure notion. Mesh requirements are established to ensure the optimality of the error estimator.