A posteriori error control for fourth-order semilinear problems with quadratic nonlinearity
Numerical Analysis
2023-09-18 v1 Numerical Analysis
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, interior penalty, and WOPSIP discretizations with piecewise quadratic polynomials.
Cite
@article{arxiv.2309.08427,
title = {A posteriori error control for fourth-order semilinear problems with quadratic nonlinearity},
author = {Carsten Carstensen and Benedikt Gräßle and Neela Nataraj},
journal= {arXiv preprint arXiv:2309.08427},
year = {2023}
}