This work was supported in part by the Department of Energy [National Nuclear Security Administration] under Award Number DE-FC52-08NA28615 and the NSF under DMS-1014817.
SIAM Journal on Numerical Analysis
Error analysis (Mathematics), Galerkin methods, Heat equation -- Numerical solutions
We give an error analysis of the recently developed DPG method applied to solve the Poisson equation and a convection-dffusion problem. We prove that the method is quasioptimal. Error estimates in terms of both the mesh size h and the polynomial degree p (for various element shapes) can be derived from our results. Results of extensive numerical experiments are also presented.
Copyright 2011 for Industrial and Applied Mathematics
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Published as: DEMKOWICZ, L., & GOPALAKRISHNAN, J. (2011). ANALYSIS OF THE DPG METHOD FOR THE POISSON EQUATION. SIAM Journal on Numerical Analysis, 49(5/6), 1788–1809. http://www.jstor.org/stable/41582671
This is the author’s version of a work that was accepted for publication in SIAM Journal on Numerical Analysis. A definitive version was subsequently published in SIAM Journal on Numerical Analysis, 2011. Vol. 49 Issue 5/6, p1788-1809.