2023/09/15 by Carsten Carstensen, Carstensen, Carsten, Benedikt Gräßle +3
Engineering · Mathematics · #65N12 #65N30 #65N50 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2309.08427
openalex publication_date 2023/09/15 · openalex created_date 2023/09/19 · openalex updated_date 2026/07/28
A general a posteriori error analysis applies to five lowest-order finite element methods for two fourth-order semi-linear problems with trilinear non-linearity and a general source. A quasi-optimal smoother extends the source term to the discrete trial space, and more importantly, modifies the trilinear term in the stream-function vorticity formulation of the incompressible 2D Navier-Stokes and the von Kármán equations. This enables the first efficient and reliable a posteriori error estimates for the 2D Navier-Stokes equations in the stream-function vorticity formulation for Morley, two discontinuous Galerkin, C0 interior penalty, and WOPSIP discretizations with piecewise quadratic polynomials.