Symmetry and Automated Branch Following for a Semilinear Elliptic PDE on a Fractal Region

@article{Neuberger2006SymmetryAA,
title={Symmetry and Automated Branch Following for a Semilinear Elliptic PDE on a Fractal Region},
author={John M. Neuberger and N{\'a}ndor Sieben and James W. Swift},
journal={SIAM J. Applied Dynamical Systems},
year={2006},
volume={5},
pages={476-507}
}

We apply the Gradient-Newton-Galerkin-Algorithm (GNGA) of Neuberger & Swift to find solutions to a semilinear elliptic Dirichlet problem on the region whose boundary is the Koch snowflake. In a recent paper, we described an accurate and efficient method for generating a basis of eigenfunctions of the Laplacian on this region. In that work, we used the symmetry of the snowflake region to analyze and post-process the basis, rendering it suitable for input to the GNGA. The GNGA uses Newton’s… CONTINUE READING