A dual mortar approach for mesh tying within a variational multiscale method for incompressible flow. (20th May 2014) - Ehrl, A.
SUMMARY In the present work, the coupling of computational subdomains with non‐conforming discretizations is addressed in the context of residual‐based variational multiscale finite element methods for incompressible fluid flow. A mortar method using dual Lagrange multipliers is introduced for handling the coupling conditions at arbitrary fluid–fluid interfaces. Recently, mortar methods have been successfully applied in the field of nonlinear solid mechanics, for example, to weakly impose interface constraints for finite deformation contact. The focus of this study is on both the integration of the dual mortar approach into an existing variational multiscale finite element framework and the investigation of the resulting interplay between variational multiscale and coupling terms. We analyze the effects of either constraining only velocity or both velocity and pressure degrees of freedom at the internal interfaces using dual Lagrange multipliers. In analogy to other problem classes, we exploit the fact that the dual mortar approach allows for an efficient condensation of the additional Lagrange multiplier degrees of freedom from the global system of equations. As a result, the typical but often undesirable saddle‐point structure of this system is completely removed. The proposed method is validated numerically for various three‐dimensional examples, including a complex patient‐specific aneurysm, and its accuracy and efficiency in comparison with standard conforming discretizations is demonstrated. Copyright © 2014 John Wiley & Sons, Ltd.