E. L. Eftang, D. B. P. Huynh,
D. J. Knezevic, E. M. Rønquist, and A. T. Patera, Adaptive Port
Reduction in Static Condensation. Proceedings of 7th Vienna Conference
on Mathematical Modelling. MATHMOD 2012 (submitted December 2011).
D. B. P. Huynh,
D. J. Knezevic, A.
T. Patera, "A Static Condensation Reduced Basis Element Method:
Approximation and A Posteriori Error Estimation," Mathematical Modelling and Numerical Analysis, revised March 2012.
D. P. B. Huynh, D. J. Knezevic, A. T.
Patera, "Certified Reduced Basis Model Characterization: a
Frequentistic Uncertainty Framework," submitted to Comput. Meth. Appl.
Mech. Eng., January 2011.
J. L. Eftang,
D. P. B. Huynh, D. J. Knezevic, A. T. Patera, “A Two-Step
Certified Reduced Basis Method,” Journal of Scientific Computing, Vol 51, Issue 1, 2012, 28-58.
D. P. B. Huynh, D. J.
Knezevic, A. T. Patera, "A Laplace Transform Certified Reduced
Basis Method; Application to the Heat Equation and Wave Equation,"
Comptes Rendus Mathematique, 349 (2011), 401-405.
D. J. Knezevic, J. W.
Peterson,
"A High Performance Parallel Implementation of the Certified Reduced
Basis Method," Comput. Meth. Appl. Mech. Eng., 200 (2011), 1455-1466.
D. P. B. Huynh, D. J. Knezevic, J. W. Peterson, A.
T. Patera,
"High-Fidelity Real-Time Simulation on Deployed Platforms," Computers and Fluids, 43(1), 2011, 74-81.
J. L. Eftang, D. J. Knezevic, A. T. Patera,
"An hp Certified Reduced Basis Method for Parametrized Parabolic
Partial Differential Equations," Mathematical and Computer
Modelling of Dynamical Systems, 4(4), 2011, DOI:
10.1080/13873954.2011.547670, 395-422.
D. J. Knezevic, "Reduced Basis Approximation and A Posteriori Error
Estimates
for a Multiscale Liquid Crystal Model," Mathematical and Computer
Modelling of Dynamical Systems, 4(4), 2011, DOI:
10.1080/13873954.2011.547676, 443-461.
D. J. Knezevic, N. C. Nguyen, A. T. Patera, "Reduced Basis
Approximation and A Posteriori Error Estimation
for the Parametrized Unsteady Boussinesq Equations," accepted to M3AS,
August 2010.
D. B. P. Huynh, D. J. Knezevic, Y. Chen, J. S. Hesthaven, A. T.
Patera, "A Natural-Norm Successive Constraint Method for inf-sup
Lower Bounds," Comput. Meth. Appl. Mech. Eng. 199 (2010), 1963–1975.
D. J. Knezevic, A. T. Patera, "A Certified Reduced Basis Method for the
Fokker-Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in
Extensional Flow," SIAM J. Sci. Comput. 32(2), 793-817, 2010.
G. F.
Carey
and D. J. Knezevic, "Multiscale and Hysteresis Effects in Vortex
Pattern Simulations for Ginzburg-Landau Problems," Internat. J.
Numer. Methods Engrg. 81 (2009), no. 7,
866-891.
D. J.
Knezevic, E. Süli, "A Heterogeneous Alternating-Direction Method
for a Micro-Macro Model of Dilute Polymeric Fluids," M2AN 43 (2009),
1117-1156.
D. J. Knezevic, E. Süli, "Spectral Galerkin Approximation
of Fokker-Planck Equations with Unbounded Drift," M2AN 43 (2009),
445-485.
D. J. Knezevic, E. Süli, "A Deterministic Multiscale Approach for
Simulating Dilute Polymeric Fluids,"
Lectures Notes in Computational Mathematics and Engineering, BAIL 2008,
Vol. 69, 23-38.
J. W. Peterson,
G. F. Carey, D. J. Knezevic, B. T. Murray, "Adaptive Finite
Element Methodology for Tumour Angiogenesis Modelling," Internat. J.
Numer. Methods Engrg. 69 (2007), no. 6, 1212-1238.