2026/07/29 by Shuonan Wu, Hao Zhou
Computer Science · Mathematics · #cs.NA #math.NA #msc:65N12 #msc:65N15 #msc:65N30
arxiv created 2026/07/29 · arxiv updated 2026/07/30
We propose an intrinsic stabilized Morley finite element method for the stream-function formulation of the surface Stokes problem on closed surfaces. The method is posed directly on a polyhedral approximation of the surface. A parameter-free jump stabilization is introduced to recover coercivity, and a discrete Korn's inequality for the trace-free Hessian is established. The main analytical contribution is a normal-separated geometric estimate for piecewise linearly approximated closed surfaces. It shows that a broad class of normal-dependent geometric consistency errors is in fact second order, even though a direct treatment suggests only first-order control. The missing order is recovered through an integral cancellation in the first normal variation. This estimate refines the standard Phν-type estimate and yields second-order consistency for the trace-free Hessian, the Stokes-type tensor Green identity, and the conormal fluxes arising in the discretization. Together with the discrete Korn's inequality, these estimates yield, under the natural H3 regularity, optimal-order convergence: first order in the broken H2 norm and second order in the broken H1 norm. As a direct consequence, the recovered tangential velocity admits a second-order L2 estimate. Numerical experiments are provided to support the theoretical results.