DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Stochastic Discontinuous Galerkin Methods (SDGM) based on fluctuation-dissipation balance

; ;
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of California, Santa Barbara, CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1574443; OSTI ID: 1633911; OSTI ID: 1817992
Report Number(s):
SAND-2019-12136J; LLNL-JRNL-770042
Journal ID: ISSN 2590-0374; S2590037419300688; 100068; PII: S2590037419300688
Grant/Contract Number:  
SC0009254; AC04-94AL85000; AC52-07NA27344
Resource Type:
Published Article
Journal Name:
Results in Applied Mathematics
Additional Journal Information:
Journal Name: Results in Applied Mathematics Journal Volume: 4 Journal Issue: C; Journal ID: ISSN 2590-0374
Country of Publication:
97 MATHEMATICS AND COMPUTING; Stochastic partial differential equations; Fluctuation-dissipation balance; Discontinuous Galerkin methods

Citation Formats

Pazner, W., Trask, N., and Atzberger, P. J. Stochastic Discontinuous Galerkin Methods (SDGM) based on fluctuation-dissipation balance. Netherlands: N. p., 2019. Web. doi:10.1016/j.rinam.2019.100068.
Pazner, W., Trask, N., & Atzberger, P. J. Stochastic Discontinuous Galerkin Methods (SDGM) based on fluctuation-dissipation balance. Netherlands.
Pazner, W., Trask, N., and Atzberger, P. J. Sun . "Stochastic Discontinuous Galerkin Methods (SDGM) based on fluctuation-dissipation balance". Netherlands.
title = {Stochastic Discontinuous Galerkin Methods (SDGM) based on fluctuation-dissipation balance},
author = {Pazner, W. and Trask, N. and Atzberger, P. J.},
abstractNote = {},
doi = {10.1016/j.rinam.2019.100068},
journal = {Results in Applied Mathematics},
number = C,
volume = 4,
place = {Netherlands},
year = {2019},
month = {12}

Works referenced in this record:

Weak Error Estimates for Trajectories of SPDEs Under Spectral Galerkin Discretization
journal, June 2018

A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier–Stokes Equations
journal, March 1997

Memory Effects in Irreversible Thermodynamics
journal, November 1961

Non-equilibrium Ginzburg-Landau model driven by colored noise
journal, March 1998

Thermal Agitation of Electricity in Conductors
journal, July 1928

Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
journal, January 2002

  • Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo
  • SIAM Journal on Numerical Analysis, Vol. 39, Issue 5
  • DOI: 10.1137/S0036142901384162

Fluctuating hydrodynamic methods for fluid-structure interactions in confined channel geometries
journal, December 2017

Finite element exterior calculus: from Hodge theory to numerical stability
journal, January 2010

  • Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
  • Bulletin of the American Mathematical Society, Vol. 47, Issue 2
  • DOI: 10.1090/S0273-0979-10-01278-4

Thermal Agitation of Electric Charge in Conductors
journal, July 1928

Partial differential equations driven by rough paths
journal, July 2009

On the foundations of the stochastic immersed boundary method
journal, April 2008

  • Kramer, Peter R.; Peskin, Charles S.; Atzberger, Paul J.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 25-28
  • DOI: 10.1016/j.cma.2007.11.010

The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
journal, January 1991

  • Cockburn, Bernardo; Shu, Chi-Wang
  • ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 25, Issue 3
  • DOI: 10.1051/m2an/1991250303371

The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
journal, December 1998

Contributions to Nonequilibrium Thermodynamics. II. Fluctuation Theory for the Boltzmann Equation
journal, January 1970

Reciprocal Relations in Irreversible Processes. I.
journal, February 1931

Multiscale temporal integrators for fluctuating hydrodynamics
journal, December 2014

Finite element and difference approximation of some linear stochastic partial differential equations
journal, May 1998

  • Allen, E. J.; Novosel, S. J.; Zhang, Z.
  • Stochastics and Stochastic Reports, Vol. 64, Issue 1-2
  • DOI: 10.1080/17442509808834159

Stochastic Reductions for Inertial Fluid-Structure Interactions Subject to Thermal Fluctuations
journal, January 2015

  • Tabak, Gil; Atzberger, Paul J.
  • SIAM Journal on Applied Mathematics, Vol. 75, Issue 4
  • DOI: 10.1137/15M1019088

Transport, Collective Motion, and Brownian Motion
journal, March 1965

Finite Element Exterior Calculus for Evolution Problems
journal, June 2017

On the accuracy of finite-volume schemes for fluctuating hydrodynamics
journal, January 2010

  • Donev, Aleksandar; Vanden-Eijnden, Eric; Garcia, Alejandro
  • Communications in Applied Mathematics and Computational Science, Vol. 5, Issue 2
  • DOI: 10.2140/camcos.2010.5.149

Nanoparticle Brownian motion and hydrodynamic interactions in the presence of flow fields
journal, July 2011

  • Uma, B.; Swaminathan, T. N.; Radhakrishnan, R.
  • Physics of Fluids, Vol. 23, Issue 7
  • DOI: 10.1063/1.3611026

The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V
journal, April 1998

  • Cockburn, Bernardo; Shu, Chi-Wang
  • Journal of Computational Physics, Vol. 141, Issue 2
  • DOI: 10.1006/jcph.1998.5892

An Analysis of the Minimal Dissipation Local Discontinuous Galerkin Method for Convection–Diffusion Problems
journal, March 2007

A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales
journal, June 2007

  • Atzberger, Paul J.; Kramer, Peter R.; Peskin, Charles S.
  • Journal of Computational Physics, Vol. 224, Issue 2
  • DOI: 10.1016/

Spatially adaptive stochastic methods for fluid–structure interactions subject to thermal fluctuations in domains with complex geometries
journal, November 2014

  • Plunkett, Pat; Hu, Jonathan; Siefert, Christopher
  • Journal of Computational Physics, Vol. 277
  • DOI: 10.1016/

Statistical inference for SPDEs: an overview
journal, February 2018

Stochastic Computational Fluid Mechanics
journal, March 2007

  • Lin, Guang; Wan, Xiaoliang; Su, Chau-hsing
  • Computing in Science and Engineering, Vol. 9, Issue 2
  • DOI: 10.1109/MCSE.2007.38

An Interior Penalty Finite Element Method with Discontinuous Elements
journal, August 1982

  • Arnold, Douglas N.
  • SIAM Journal on Numerical Analysis, Vol. 19, Issue 4
  • DOI: 10.1137/0719052

Stochastic Cahn-Hilliard equation
journal, January 1996

  • Da Prato, Giuseppe; Debussche, Arnaud
  • Nonlinear Analysis: Theory, Methods & Applications, Vol. 26, Issue 2
  • DOI: 10.1016/0362-546X(94)00277-O

Staggered Schemes for Fluctuating Hydrodynamics
journal, January 2012

  • Balboa, Florencio; Bell, John B.; Delgado-Buscalioni, Rafael
  • Multiscale Modeling & Simulation, Vol. 10, Issue 4
  • DOI: 10.1137/120864520

Discontinuous Galerkin approximations for elliptic problems
journal, January 2000

Spatially adaptive stochastic numerical methods for intrinsic fluctuations in reaction–diffusion systems
journal, May 2010

Analysis and numerical solution of stochastic phase-field models of tumor growth: Stochastic Tumor Growth
journal, October 2014

  • Lima, Ernesto A. B. F.; Almeida, Regina C.; Oden, J. Tinsley
  • Numerical Methods for Partial Differential Equations, Vol. 31, Issue 2
  • DOI: 10.1002/num.21934

Asymptotic statistical inference for a stochastic heat flow problem
journal, July 1985

TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems
journal, September 1989

Fluctuating Hydrodynamics Methods for Dynamic Coarse-Grained Implicit-Solvent Simulations in LAMMPS
journal, January 2016

  • Wang, Y.; Sigurdsson, J. K.; Atzberger, P. J.
  • SIAM Journal on Scientific Computing, Vol. 38, Issue 5
  • DOI: 10.1137/15M1026390

Stochastic Eulerian Lagrangian methods for fluid–structure interactions with thermal fluctuations
journal, April 2011

Stochastic Phase Field Equations: Existence and Uniqueness
journal, March 2002

Irreversibility and Generalized Noise
journal, July 1951

Numerical Approximation of Some Linear Stochastic Partial Differential Equations Driven by Special Additive Noises
journal, January 2002

Statistical inference for stochastic parabolic equations: a spectral approach
journal, January 2009