# G. Karniadakis

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- Publications
- Influence

The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations

- D. Xiu, G. Karniadakis
- Mathematics, Computer Science
- SIAM J. Sci. Comput.
- 1 February 2002

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Spectral/hp Element Methods for Computational Fluid Dynamics

- G. Karniadakis, S. Sherwin
- Mathematics
- 11 August 2005

Introduction Fundamental concepts in one dimension Multi-dimensional expansion bases Multi-dimensional formulations Diffusion equation Advection and advection-diffusion Non-conforming elements… Expand

High-order splitting methods for the incompressible Navier-Stokes equations

- G. Karniadakis, M. Israeli, S. A. Orszag
- Mathematics
- 1 December 1991

Abstract A new pressure formulation for splitting methods is developed that results in high-order time-accurate schemes for the solution of the incompressible Navier-Stokes equations. In particular,… Expand

REPORT: A MODEL FOR FLOWS IN CHANNELS, PIPES, AND DUCTS AT MICRO AND NANO SCALES

- A. Beskok, G. Karniadakis
- Physics
- 1 February 1999

Rarefied gas flows in channels, pipes, and ducts with smooth surfaces are studied in a wide range of Knudsen number (Kn) at low Mach number (M) with the objective of developing simple, physics-based… Expand

Spectral/hp Element Methods for CFD

- G. Karniadakis, S. Sherwin
- Mathematics
- 15 April 1999

Introduction Fundamental concepts in one dimension Multi-dimensional expansion bases Multi-dimensional formulations Diffusion equation Advection and advection-diffusion Non-conforming elements… Expand

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

- M. Raissi, P. Perdikaris, G. Karniadakis
- Mathematics, Computer Science
- J. Comput. Phys.
- 1 February 2019

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Modeling uncertainty in flow simulations via generalized polynomial chaos

- D. Xiu, G. Karniadakis
- Mathematics
- 1 May 2003

We present a new algorithm to model the input uncertainty and its propagation in incompressible flow simulations. The stochastic input is represented spectrally by employing orthogonal polynomial… Expand

An adaptive multi-element generalized polynomial chaos method for stochastic differential equations

- Xiaoliang Wan, G. Karniadakis
- Mathematics
- 1 November 2005

We formulate a Multi-Element generalized Polynomial Chaos (ME-gPC) method to deal with long-term integration and discontinuities in stochastic differential equations. We first present this method for… Expand

Dynamics and low-dimensionality of a turbulent near wake

- X. Ma, G.-S. Karamanos, G. Karniadakis
- Physics
- 10 May 2000

We investigate the dynamics of the near wake in turbulent flow past a circular cylinder up to ten cylinder diameters downstream. The very near wake (up to three diameters) is dominated by the shear… Expand

The Development of Discontinuous Galerkin Methods

- B. Cockburn, G. Karniadakis, C. Shu
- Computer Science
- 2000

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