2025/08/18 by Nochetto, Ricardo H., Shakipov, Mansur · 1 citation
#35J47 #35J50 #58J05 #65N30 #Analysis of PDEs (math.AP) #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2508.13342
For a d-dimensional hypersurface of class C3 without boundary, we reformulate the surface Stokes equations as a nonsymmetric indefinite elliptic problem governed by two Laplacians. We then use this elliptic reformulation as a basis for a numerical method based on lifted parametric FEM. Assuming no geometric error for simplicity, we prove its well-posedness, quasi-best approximation in a robust mesh-dependent H1-norm for any polynomial degree, as well as an optimal L2 error estimate for both velocity and pressure. This entails a sufficiently small mesh size that solely depends on the Weingarten map and circumvents the usual discrete inf-sup condition. We present numerical experiments for velocity-pressure pairs with equal and disparate polynomial degrees, demonstrating that the proposed method is both accurate and practical.