Abstract
Author(s): Craig, Katy; Bertozzi, Andrea L | Abstract: Motivated by classical vortex methods for the Euler equations, we develop a numerical method for the aggregation equation. This provides a counterpoint to existing literature on particle methods. By regularizing the velocity field with a mollifier or blob function, the method has a faster rate of convergence and allows a wider range of admissible kernels. In fact, we prove arbitrarily high polynomial rates of convergence to classical solutions, depending on the choice of mollifier. The method conserves mass and the corresponding particle system is both energy decreasing for a regularized free energy functional and preserves the Wasserstein gradient flow structure. We consider numerical examples that validate our predicted rate of convergence and illustrate qualitative properties of the method.
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