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Published October 15, 2015 | public
Journal Article

A minimum Sobolev norm technique for the numerical discretization of PDEs

Abstract

Partial differential equations (PDEs) are discretized into an under-determined system of equations and a minimum Sobolev norm solution is shown to be efficient to compute and converge under very generic conditions. Numerical results of a single code, that can handle PDEs in first-order form on complicated polygonal geometries, are shown for a variety of PDEs: variable coefficient div–curl, scalar elliptic PDEs, elasticity equation, stationary linearized Navier–Stokes, scalar fourth-order elliptic PDEs, telegrapher's equations, singular PDEs, etc.

Additional Information

© 2015 Elsevier. Received 4 July 2013; Received in revised form 9 March 2015; Accepted 6 July 2015; Available online 20 July 2015. This material is based upon work supported by the National Science Foundation under Grant Nos. CCF-0830604 and CCF-1450321. The research of this author was supported, in part, by Grant DMS-0908037 from the National Science Foundation and Grant W911NF-09-1-0465 from the U.S. Army Research Office. We would like to thank Professors Yu Chen, Froilan Dopico, Ming Gu and John Strain for useful discussions. We would also like to thank Karthik Jayaraman Raghuram and Joseph Moffitt for help with the early experiments and code[7,20].

Additional details

Created:
August 20, 2023
Modified:
October 24, 2023