An edge‐based pressure stabilization technique for finite elements on arbitrarily anisotropic meshes

Summary In this paper, we analyze a stabilized equal‐order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a subdomain, for example, along the boundary of the domain, with the only condition that a maximum angle is fulfilled in each element. This discretization is motivated by applications on moving domains as arising, for example, in fluid‐structure interaction or multiphase‐flow problems. To deal with the anisotropies, we define a modification of the original continuous interior penalty stabilization approach. We show analytically the discrete stability of the method and convergence of order in the energy norm and in the L2‐norm of the velocities. We present numerical examples for a linear Stokes problem and for a nonlinear fluid‐structure interaction problem, which substantiate the analytical results and show the capabilities of the approach.