A Blob Method for the Aggregation Equation

Understand

Motivated by classical vortex blob methods for the Euler equations, we develop a numerical blob 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 blob 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.