Model order reduction in fluid dynamics: challenges and perspectives
This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems
are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit …
are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit …
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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Advertisement SpringerLink Account Menu Find a journal Publish with us Track your research …
A class of discontinuous Petrov–Galerkin methods. II. Optimal test functions
L Demkowicz, J Gopalakrishnan - Numerical Methods for …, 2011 - Wiley Online Library
We lay out a program for constructing discontinuous Petrov–Galerkin (DPG) schemes
having test function spaces that are automatically computable to guarantee stability. Given a …
having test function spaces that are automatically computable to guarantee stability. Given a …
[HTML][HTML] 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 Variational Physics-Informed Neural Networks
We introduce a Robust version of the Variational Physics-Informed Neural Networks method
(RVPINNs). As in VPINNs, we define the quadratic loss functional in terms of a Petrov …
(RVPINNs). As in VPINNs, we define the quadratic loss functional in terms of a Petrov …
Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics
We present hybridizable discontinuous Galerkin methods for solving steady and time-
dependent partial differential equations (PDEs) in continuum mechanics. The essential …
dependent partial differential equations (PDEs) in continuum mechanics. The essential …
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 …
Adaptive Petrov--Galerkin methods for first order transport equations
We propose stable variational formulations for certain linear, unsymmetric operators with first
order transport equations in bounded domains serving as the primary focus of this paper …
order transport equations in bounded domains serving as the primary focus of this paper …
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics
We present a class of hybridizable discontinuous Galerkin (HDG) methods for the numerical
simulation of wave phenomena in acoustics and elastodynamics. The methods are fully …
simulation of wave phenomena in acoustics and elastodynamics. The methods are fully …
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 …