An overview of the discontinuous Petrov Galerkin method
LF Demkowicz, J Gopalakrishnan - Recent Developments in …, 2014 - Springer
An Overview of the Discontinuous Petrov Galerkin Method | SpringerLink Skip to main content
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Variational multiscale stabilization and the exponential decay of fine-scale correctors
D Peterseim - Building bridges: connections and challenges in …, 2016 - Springer
This paper reviews the variational multiscale stabilization of standard finite element methods
for linear partial differential equations that exhibit multiscale features. The stabilization is of …
for linear partial differential equations that exhibit multiscale features. The stabilization is of …
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 …
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 …
Eliminating the pollution effect in Helmholtz problems by local subscale correction
D Peterseim - Mathematics of Computation, 2017 - ams.org
We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of
the Helmholtz equation with large wave number $\kappa $ in bounded domains in $\mathbb …
the Helmholtz equation with large wave number $\kappa $ in bounded domains in $\mathbb …
A new weak Galerkin finite element method for the Helmholtz equation
An absolutely stable weak Galerkin (WG) finite element method is introduced and analysed
for the Helmholtz equation. This means that the stability and well-posedness of the method …
for the Helmholtz equation. This means that the stability and well-posedness of the method …
Preasymptotic Error Analysis of CIP-FEM and FEM for Helmholtz Equation with High Wave Number. Part II: Version
L Zhu, H Wu - SIAM Journal on Numerical Analysis, 2013 - SIAM
In this paper, which is the second in a series of two, the preasymptotic error analysis of the
continuous interior penalty finite element method (CIP-FEM) and the FEM for the Helmholtz …
continuous interior penalty finite element method (CIP-FEM) and the FEM for the Helmholtz …
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 …
[HTML][HTML] Neural control of discrete weak formulations: Galerkin, least squares & minimal-residual methods with quasi-optimal weights
There is tremendous potential in using neural networks to optimize numerical methods. In
this paper, we introduce and analyze a framework for the neural optimization of discrete …
this paper, we introduce and analyze a framework for the neural optimization of discrete …
Preasymptotic error analysis of higher order FEM and CIP-FEM for Helmholtz equation with high wave number
Y Du, H Wu - SIAM Journal on Numerical Analysis, 2015 - SIAM
A preasymptotic error analysis of the finite element method (FEM) and some continuous
interior penalty finite element method (CIP-FEM) for the Helmholtz equation in two and three …
interior penalty finite element method (CIP-FEM) for the Helmholtz equation in two and three …