SIAM Journal on Numerical Analysis · 2011 · 132 citations · 20 references
ComputingComputational EngineeringPhysicsComputational MechanicsDifferential EquationsFinite Element MethodsConvergence AnalysisError EstimationFinite Element DiscretizationFinite Element FormulationNumerical Methods For Differential EquationsPartial Differential EquationsConvectionConvection-diffusionConvection-diffusion ModelingMesh SizeNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsPoisson EquationPoisson's Equation
We give an error analysis of the recently developed DPG method applied to solve the Poisson equation and a convection-diffusion 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.
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Bernardo Cockburn, Jay Gopalakrishnan, Raytcho Lazarov · SIAM Journal on Numerical Analysis · 2009 · 1.2K citations
Computing, Computational Engineering, Computational Mechanics +7