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.
Demkowicz, Leszek and Gopalakrishnan, Jay, "Analysis of the DPG Method for the Poisson Equation" (2011). Mathematics and Statistics Faculty Publications and Presentations. 42.