An enriched finite element method is described for capillary hydrodynamics including dynamic wetting. The method is enriched via the Conformal Decomposition Finite Element Method (CDFEM). Two formulations are described, one with first-order accuracy and one with second-order accuracy in time. Both formulations utilize a semi-implicit form for the surface tension that is shown to effectively circumvent the explicit capillary time step limit. Sharp interface boundary conditions are developed for capturing the dynamic contact angle as the fluid interface moves along the wall. By virtue of the CDFEM, the contact line is free to move without risk of mesh tangling, but is sharply captured. Multiple problems are used to demonstrate the effectiveness of the methods.

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