An overview of the discontinuous Petrov Galerkin method
LF Demkowicz, J Gopalakrishnan - Recent Developments in …, 2014 - Springer
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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 …
Coercive space-time finite element methods for initial boundary value problems
O Steinbach, M Zank - Electronic Transactions on Numerical …, 2020 - etna.ricam.oeaw.ac.at
We propose and analyse new space-time Galerkin-Bubnov-type finite element formulations
of parabolic and hyperbolic second-order partial differential equations in finite time intervals …
of parabolic and hyperbolic second-order partial differential equations in finite time intervals …
A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity
We continue our theoretical and numerical study on the Discontinuous Petrov–Galerkin
method with optimal test functions in context of 1D and 2D convection-dominated diffusion …
method with optimal test functions in context of 1D and 2D convection-dominated diffusion …
A computational study of the weak Galerkin method for second-order elliptic equations
The weak Galerkin finite element method is a novel numerical method that was first
proposed and analyzed by Wang and Ye (2011) for general second order elliptic problems …
proposed and analyzed by Wang and Ye (2011) for general second order elliptic problems …
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 …
[HTML][HTML] A robust DPG method for convection-dominated diffusion problems II: Adjoint boundary conditions and mesh-dependent test norms
We introduce a DPG method for convection-dominated diffusion problems. The choice of a
test norm is shown to be crucial to achieving robust behavior with respect to the diffusion …
test norm is shown to be crucial to achieving robust behavior with respect to the diffusion …
A spacetime DPG method for the Schrodinger equation
L Demkowicz, J Gopalakrishnan, S Nagaraj… - SIAM Journal on …, 2017 - SIAM
A spacetime discontinuous Petrov--Galerkin (DPG) method for the linear time-dependent
Schrödinger equation is proposed. The spacetime approach is particularly attractive for …
Schrödinger equation is proposed. The spacetime approach is particularly attractive for …