{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:27:34Z","timestamp":1776846454259,"version":"3.51.2"},"reference-count":73,"publisher":"American Mathematical Society (AMS)","issue":"300","license":[{"start":{"date-parts":[[2016,12,4]],"date-time":"2016-12-04T00:00:00Z","timestamp":1480809600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1401867"],"award-info":[{"award-number":["1401867"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>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 \u201cblob function\u201d, 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. The blob method conserves mass and the corresponding particle system is 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.<\/p>","DOI":"10.1090\/mcom3033","type":"journal-article","created":{"date-parts":[[2015,2,4]],"date-time":"2015-02-04T10:52:50Z","timestamp":1423047170000},"page":"1681-1717","source":"Crossref","is-referenced-by-count":56,"title":["A blob method for the aggregation equation"],"prefix":"10.1090","volume":"85","author":[{"given":"Katy","family":"Craig","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Bertozzi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,12,4]]},"reference":[{"key":"1","series-title":"Lectures in Mathematics ETH Z\\\"{u}rich","isbn-type":"print","volume-title":"Gradient flows in metric spaces and in the space of probability measures","author":"Ambrosio, Luigi","year":"2008","ISBN":"https:\/\/id.crossref.org\/isbn\/9783764387211","edition":"2"},{"issue":"11","key":"2","doi-asserted-by":"publisher","first-page":"1495","DOI":"10.1002\/cpa.20223","article-title":"A gradient flow approach to an evolution problem arising in superconductivity","volume":"61","author":"Ambrosio, Luigi","year":"2008","journal-title":"Comm. 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