An overview of the discontinuous Petrov Galerkin method
LF Demkowicz, J Gopalakrishnan - Recent Developments in …, 2014 - Springer
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[图书][B] Finite elements II
A Ern, JL Guermond - 2021 - Springer
The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …
impact of computer technology, the growing importance of computer modelling and the …
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 …
A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations
We introduce the concept of machine-learning minimal-residual (ML-MRes) finite element
discretizations of partial differential equations (PDEs), which resolve quantities of interest …
discretizations of partial differential equations (PDEs), which resolve quantities of interest …
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 …
[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 …
An HDG method for linear elasticity with strong symmetric stresses
This paper presents a new hybridizable discontinuous Galerkin (HDG) method for linear
elasticity on general polyhedral meshes, based on a strong symmetric stress formulation …
elasticity on general polyhedral meshes, based on a strong symmetric stress formulation …
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 …
Wavenumber explicit analysis of a DPG method for the multidimensional Helmholtz equation
We study the properties of a novel discontinuous Petrov Galerkin (DPG) method for acoustic
wave propagation. The method yields Hermitian positive definite matrices and has good pre …
wave propagation. The method yields Hermitian positive definite matrices and has good pre …
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 …