An overview of the discontinuous Petrov Galerkin method
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Breaking spaces and forms for the DPG method and applications including Maxwell equations
C Carstensen, L Demkowicz… - Computers & Mathematics …, 2016 - Elsevier
Abstract Discontinuous Petrov–Galerkin (DPG) methods are made easily implementable
using “broken” test spaces, ie, spaces of functions with no continuity constraints across mesh …
using “broken” test spaces, ie, spaces of functions with no continuity constraints across mesh …
An analysis of the practical DPG method
J Gopalakrishnan, W Qiu - Mathematics of Computation, 2014 - ams.org
We give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method,
accounting for all the approximations made in its practical implementation. Specifically, we …
accounting for all the approximations made in its practical implementation. Specifically, we …
A class of discontinuous Petrov–Galerkin methods. Part IV: The optimal test norm and time-harmonic wave propagation in 1D
The phase error, or the pollution effect in the finite element solution of wave propagation
problems, is a well known phenomenon that must be confronted when solving problems in …
problems, is a well known phenomenon that must be confronted when solving problems in …
Adaptivity and variational stabilization for convection-diffusion equations∗
In this paper we propose and analyze stable variational formulations for convection diffusion
problems starting from concepts introduced by Sangalli. We derive efficient and reliable a …
problems starting from concepts introduced by Sangalli. We derive efficient and reliable a …
Analysis of the DPG method for the Poisson equation
L Demkowicz, J Gopalakrishnan - SIAM Journal on Numerical Analysis, 2011 - SIAM
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 …
Poisson equation and a convection-diffusion problem. We prove that the method is …
A posteriori error control for DPG methods
A combination of ideas in least-squares finite element methods with those of hybridized
methods recently led to discontinuous Petrov--Galerkin (DPG) finite element methods. They …
methods recently led to discontinuous Petrov--Galerkin (DPG) finite element methods. They …
Robust DPG method for convection-dominated diffusion problems
L Demkowicz, N Heuer - SIAM Journal on Numerical Analysis, 2013 - SIAM
We propose and analyze a discontinuous Petrov--Galerkin (DPG) method for convection-
dominated diffusion problems that provides robust L^2 error estimates for the field variables …
dominated diffusion problems that provides robust L^2 error estimates for the field variables …
[BOOK][B] Multiscale Model Reduction
The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modeling and the …
impact of computer technology, the growing importance of computer modeling and the …
The moving discontinuous Galerkin finite element method with interface condition enforcement for compressible viscous flows
AD Kercher, A Corrigan… - International Journal for …, 2021 - Wiley Online Library
The moving discontinuous Galerkin finite element method with interface condition
enforcement is applied to the case of viscous flows. This method uses a weak formulation …
enforcement is applied to the case of viscous flows. This method uses a weak formulation …