Stability and convergence analysis for intrinsic surface Stokes discretizations

Establish a detailed stability and convergence analysis for the intrinsic surface Stokes discretization based on exactly tangential, nodal grad-conforming vector-valued finite element spaces and the associated H1 vector Laplacian problems.

Background

The intrinsic framework applies the nodal grad-conforming construction to the surface Stokes problem. The construction enforces exact tangency and nodal inter-chart continuity, while allowing interface jumps when transmission maps vary along chart interfaces. Numerical results indicate the expected convergence rates for velocity, pressure, broken gradient, and interface-jump norms.

Despite these numerical observations and the jump estimate, the paper does not provide a mathematical stability or convergence theory for the surface Stokes method or for the related H1 vector Laplacian problems. Such an analysis would justify the observed rates and clarify the effect of nonconformity at chart interfaces.