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arXiv · 2309.08427

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

Carsten Carstensen·Benedikt Gräßle·Neela Nataraj
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Abstract

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 K\'{a}rm\'{a}n 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.

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Carsten Carstensen, Benedikt Gräßle, Neela Nataraj. 2023-09-15. A posteriori error control for fourth-order semilinear problems with quadratic nonlinearity. https://arxiv.org/abs/2309.08427

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