Fetching the paper…
Reading the bibliography…
The numerical approximation of solutions of parametric or stochastic hyperbolic PDEs is still a serious challenge.
Turbulence and the dynamics of coherent structures, parts I-III
Lawrence Sirovich · 1987
Earlier work this paper cites.
The h, p and h-p version of the finite element method; basis theory and applications
I. Babuška and B.Q. Guo · 1992
Earlier work this paper cites.
p- and hp- Finite Element Methods: Theory and Applications to Solid and Fluid Mechanics
Christoph Schwab · 1999
Earlier work this paper cites.
h p hp -finite element methods for hyperbolic problem
E. Süli, P. Houston, and C. Schwab · 2000
Earlier work this paper cites.
Galerkin proper orthogonal decomposition methods for parabolic problems
K. Kunisch and S. Volkwein · 2001
Earlier work this paper cites.
Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics
K. Kunisch and S. Volkwein · 2002
Earlier work this paper cites.
The wiener–askey polynomial chaos for stochastic differential equations
Dongbin Xiu and George Em Karniadakis · 2002
Earlier work this paper cites.
Galerkin finite element approximations of stochastic elliptic partial differential equations
Ivo Babuška, Raúl Tempone, and Georgios E. Zouraris · 2004
Earlier work this paper cites.
Sparse grids
Hans-Joachim Bungartz and Michael Griebel · 2004
Earlier work this paper cites.
Uncertainty analysis for the steady-state flows in a dual throat nozzle
Qian-Yong Chen, David Gottlieb, and Jan S. Hesthaven · 2005
Earlier work this paper cites.
Computing with Hp-Adaptive Finite Elements, Vol. 1: One and Two Dimensional Elliptic and Maxwell Problems
Leszek Demkowicz · 2006
Earlier work this paper cites.
“natural norm” a posteriori error estimators for reduced basis approximations
S. Sen, K. Veroy, D.B.P. Huynh, S. Deparis, N.C. Nguyen, and A.T. Patera · 2006
Earlier work this paper cites.
A stochastic collocation method for elliptic partial differential equations with random input data
Ivo Babuška, Fabio Nobile, and Raúl Tempone · 2007
Earlier work this paper cites.
Deal.ii – a general-purpose object-oriented finite element library
W. Bangerth, R. Hartmann, and G. Kanschat · 2007
Earlier work this paper cites.
Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations
A.T. Patera and G. Rozza · 2007
Earlier work this paper cites.
Reduced basis method for explicit finite volume approximations of nonlinear conservation laws
B. Haasdonk and M. Ohlberger · 2008
Earlier work this paper cites.
Reduced basis method for finite volume approximations of parametrized linear evolution equations
Bernard Haasdonk and Mario Ohlberger · 2008
Earlier work this paper cites.
Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
G. Rozza, D.B.P. Huynh, and A.T. Patera · 2008
Earlier work this paper cites.
Reduced basis approximation and a posteriori error estimation for the time-dependent viscous burgers’ equation
Ngoc-Cuong Nguyen, Gianluigi Rozza, and AnthonyT. Patera · 2009
Cited alongside, same era.
Convergence rates of best n-term galerkin approximations for a class of elliptic spdes
Albert Cohen, Ronald DeVore, and Christoph Schwab · 2010
Cited alongside, same era.
An “ h p hp ” certified reduced basis method for parametrized elliptic partial differential equations
Jens L. Eftang, Anthony T. Patera, and Einar M. Rønquist · 2010
Cited alongside, same era.
Numerical methods for uncertainty propagation in high speed flows
Gianluca Iaccarino, Per Pettersson, Jan Nordström, and Jeroen Witteveen · 2010
Cited alongside, same era.
Efficiency of shock capturing schemes for burgers’ equation with boundary uncertainty
Per Pettersson, Qaisar Abbasb, Gianluca Iaccarino, and Jan Nordström · 2010
Cited alongside, same era.
A comparison of hp-adaptive strategies for elliptic partial differential equations
William F. Mitchell and Marjorie A. McClain · 2014
Later among the works it cites.
Stabilized reduced basis method for parametrized advection–diffusion PDEs
Paolo Pacciarini and Gianluigi Rozza · 2014
Later among the works it cites.
A stochastic galerkin method for the euler equations with roe variable transformation
Per Pettersson, Gianluca Iaccarino, and Jan Nordström · 2014
Later among the works it cites.
A space-time hp-interpolation-based certified reduced basis method for burgers’ equation
Masayuki Yano, Anthony T. Patera, and Karsten Urban · 2014
Later among the works it cites.
TensorFlow: Large-scale machine learning on heterogeneous systems, 2015
Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath Kudlur, Josh Levenberg, Dan Mané, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, Mike Schuster, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viégas, Oriol Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng · 2015
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Analytic regularity and polynomial approximation of parametric and stochastic elliptic pdes
Albert Cohen, Ronald DeVore, and Christoph Schwab · 2011
Cited alongside, same era.
Reduced order models for parameterized hyperbolic conservations laws with shock reconstruction
P.G. Constantine and G. Iaccarino · 2012
Cited alongside, same era.
Parameter multi-domain ‘hp’ empirical interpolation
Jens L. Eftang and Benjamin Stamm · 2012
Cited alongside, same era.
Reduced-order modeling based on approximated lax pairs
Jean-Frédéric Gerbeau and Damiano Lombardi · 2012
Cited alongside, same era.
Sparse tensor multi-level monte carlo finite volume methods for hyperbolic conservation laws with random initial data
S. Mishra and Ch. Schwab · 2012
Cited alongside, same era.
Generalised polynomial chaos for a class of linear conservation laws
Roland Pulch and Dongbin Xiu · 2012
Cited alongside, same era.
Adaptive anisotropic spectral stochastic methods for uncertain scalar conservation laws
J. Tryoen, O. Le Maître, and A. Ern · 2012
Cited alongside, same era.
Later among the works it cites.
Remi Abgrall and David Amsallem · 2015
Later among the works it cites.
Approximation of high-dimensional parametric pdes
Albert Cohen and Ronald DeVore · 2015
Later among the works it cites.
How to best sample a solution manifold?
Wolfgang Dahmen · 2015
Later among the works it cites.
Measure Theory and Fine Properties of Functions
Lawrence Craig Evans and Ronald F. Gariepy · 2015
Later among the works it cites.
Chebyshev interpolation for parametric option pricing
Maximilian Gaß, Kathrin Glau, Mirco Mahlstedt, and Maximilian Mair · 2015
Later among the works it cites.
The shifted proper orthogonal decomposition: A mode decomposition for multiple transport phenomena
Julius Reiss, Philipp Schulze, and Jörn Sesterhenn · 2015
Later among the works it cites.
Reduced basis techniques for nonlinear conservation laws
Taddei, T., Perotto, S., and Quarteroni, A · 2015
Later among the works it cites.
Model Order Reduction for Problems with large Convection Effects
Nicolas Cagniart, Yvon Maday, and Benjamin Stamm · 2016
Later among the works it cites.
A well-balanced stochastic galerkin method for scalar hyperbolic balance laws with random inputs
Shi Jin, Dongbin Xiu, and Xueyu Zhu · 2016
Later among the works it cites.
Reduced basis methods: Success, limitations and future challenges
Mario Ohlberger and Stephan Rave · 2016
Later among the works it cites.
Openfoam: Tutorial guide, 2017
2017
Closest in time.
Transport reversal for model reduction of hyperbolic partial differential equations
Donsub Rim, Scott Moe, and Randall J LeVeque · 2017
Closest in time.
Interpolation of functions with parameter dependent jumps by transformed snapshots
G. Welper · 2017
Closest in time.