A posteriori error control for fourth-order semilinear problems with quadratic nonlinearity

09/15/2023

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by   Carsten Carstensen, et al.

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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, C^0 interior penalty, and WOPSIP discretizations with piecewise quadratic polynomials.