Citations (as of Spring 2007)
Monograph "Higher-Order Finite Element Methods"
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M. Brasher, R. Haimes: Rendering Planar Cuts Through Quadratic and Cubic
Finite Elements, Proceedings of IEEE Visualization 2004 (VIS'04),
October 10 - 15, 2004 Austin, Texas, pp. 409-416.
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T. Eibner, J.M. Melenk: Use of higher-order shape functions in the scaled
boundary finite element method. Report, University of Reading, 2005.
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K.J. Fidkowski: A high-order discontinuous Galerkin multigrid solver for
aerodynamic applications, Master's Thesis, Massachussetts Institute of
Technology.
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J.S. Hesthaven, T. Warburton: High order nodal discontinuous
Galerkin methods for the Maxwell eigenvalue problem,
Phil. Trans. Math. Phys. Engrg. Sci., Vol. 362, 2004, pp. 493 - 524.
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J.J. Heys, T.A. Manteuffel, S.F. McCormick, L.N. Olson: Algebraic Multigrid (AMG) for Higher-Order Finite Elements,
Journal of Computational Physics, to appear.
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P.D. Ledger, K. Morgan: The Application of the hp–Finite Element Method to
Electromagnetic Problems, Invited review article for Archives of Computational
Methods in Science and Engineering, August 2004.
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Yves Renard, Julien Pommier: Documentation to GETFEM++, Part 3,
A Generic Finite Element Library in C++,
Description of Finite Element and Integration Methods,
Toulouse, France, 2004.
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M.A. Taylor, B.A. Wingate, L.P. Bos: Several new quadrature formulas for
polynomial integration in the triangle, submitted.
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M.A. Taylor, B.A. Wingate, L. Bos: A Cardinal Function Algorithm for Computing
Multivariate Quadrature Points, SIAM J. Numer. Anal., 2005.
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T.H. Vu, A.J. Deeks: Use of higher-order shape functions in the scaled
boundary finite element method.
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T. Warburton, M. Embree: The Role of the Penalty in the
Local Discontinuous Galerkin Method for
Maxwell’s Eigenvalue Problem, submitted to Elsevier November 2004.
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Listed in Author Index of Finite Element Books,
Linkoping Institute of Technology,
http://www.solid.ikp.liu.se/fe/auth.html
Paper [JP-2004-5]:
Goal-Oriented hp-Adaptivity for Elliptic
Problems
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W. Cecot, W. Rachowicz, L. Demkowicz: An hp-adaptive finite
element method for electromagnetics, Part 3, Int. J.
Numer. Meth. Engng 2003; 57; DOI: 10.1002/nme.713.
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L. Demkowicz: Fully Automatic hp-Adaptive Simulations for Maxwell's
Equations, Book of Abstracts, International Workshop on Numerical
and Symbolic Scientific Computing, June 16 - 21, St. Wolfgang, Austria.
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D. Pardo, L. Demkowicz, C. Torres-Verdin, M. Paszynski: A Self-Adaptive
Goal-Oriented
hp Finite Element method with Electromagnetic Applications. Part II:
Electrodynamics. CMAME, 2006.
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D. Pardo, L. Demkowicz, C. Torres-Verdin, M. Paszynski: Simulation of
Resistivity Logging-While-Drilling (LWD) Measurements Using a
Self-Adaptive Goal-Oriented hp Finite Element Method. SIAM Journal on
Applied Mathematics, submitted, 2005.
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D. Pardo, L. Demkowicz, C. Torres-Verdin, L. Tabarovsky,
A Goal Oriented HP-Adaptive Finite Element Strategy with Electromagnetic
Applications. Part I: Electrostatics.
"International Journal for Numerical Methods in Engineering, in press
(available online), Dec 2004.
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D. Pardo, C. Torres-Verdin, L. Demkowicz,
Comparison of a Goal-Oriented hp-Adaptive Strategy vs. a Radial Code.
Report, Nov 2005.
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D. Pardo, C. Torres-Verdin, L. Demkowicz,
Using a Goal-Oriented hp-Adaptive Strategy to Solve a DC Resistivity Logging
Model Problem.
Baker-Atlas Report, July 2004
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D. Pardo, L. Demkowicz,
Fully Automatic Goal-Oriented hp-Adaptivity for Elliptic Problems.
Baker-Atlas Report, May 2004
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D. Pardo,
An hp-Adaptive Finite Element (FE) Method for Solving Electromagnetic (EM)
Problems. Part I: Petroleum Engineering Applications.
Baker-Atlas Report, 2003
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M. Paszynski, L. Demkowicz, D. Pardo,
Verification of Goal-Oriented hp-Adaptivity.
"Computers and Mathematics with Applications, accepted, 2005
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J. Pardo: Integration of hp-Adaptivity With a Two-Grid Solver:
Applications to Electromagnetics, Dissertation Proposal,
The University of Texas at Austin, 2002.
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J.T. Oden, S. Prudhomme, L. Demkowicz:
A Posteriori Error Estimation for Acoustic Wave Propagation Problems.
Paper [JP-2001-1]: On One Approach to A-Posteriori
Error Estimates for Evolution Problems Solved by the Method
of Lines
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I. Babuska and S. Ohnimus:
A posteriori error estimation for the semidiscrete finite
element method of parabolic differential equations, Computer Methods in
Applied Mechanics and Engineering 190 (June 2001), No. 35-36, pp. 4691-4712.
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J. de Frutos, J. Novo:
A posteriori error estimation with the p-version of
the finite element method for nonlinear parabolic differential equations,
Comput Methods Appl. Mech. Engrg. 191 (43): 4893-4904, 2002.
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J. de Frutos, J. Novo: Element-wise a posteriori estimates based on
hierarchical bases for non-linear parabolic problems, Int.
J. Numer. Meth. Engng (in press).
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O. Lakris, C. Makridakis: Elliptic Reconstruction and A-Posteriori Error
Estimates for Fully Discrete Linear Parabolic...,
A European Union Research and Training Network, online preprint.
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C. Makridakis, R.H. Nochetto: Elliptic Reconstruction and A-Posteriori Error
Estimates for Parabolic Problems, SIAM J. Numer. Anal., 2003.
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P.K. Moore: Implicit
Interpolation Error-Based Error Estimation Strategy in 2D, SMUM Report,
Texas Southern Methodist University.
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A Complete Bibliography of Publications in Numerische Mathematik,
Nelson HF Beebe Center for Scientific Computing, math.utah.edu.
Paper [CP-2005-2]: P. Karban, I. Dolezel, P. Solin:
Computation of General Nonstationary 2D Eddy Currents in Linear Moving
Arrangements Using an Integro-Differential Approach
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P. Karban: Solution of Nonstationary Eddy Current Problems by Integral
Techniques. Report, University of West Bohemia, 2005.
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P. Karban, J. Barglik: Techniques of Processing Solid and Liquid Metals Based
on Electromagnetic Induction. Report, University of West Bohemia, 2005.
Paper [JP-SUBM-5]: On a Discrete Maximum Principle for hp-FEM,
submitted
- J. Karatson, S. Korotov, M. Krizek:
On Discrete Maximum Principles for Nonlinear Elliptic Problems, submitted.
Paper [JP-2003-1]: Application of the
Method of Lines to Unsteady Compressible Euler Equations
- D.R. Fuhrman, H.B. Bingham, P.A. Madsen, P.G. Thomsen:
Linear and nonlinear stability analysis for finite
difference discretizations of high-order...,
Int. J. Numer. Meth. Fluids 2004; 45: DOI: 10.1002/d.713.
Paper [JP-2000-3]:
Induction Heating of Thin Slabs in Nonmagnetic Media
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A Complete Bibliography of Lecture Notes in Computational Science and
Engineering. Nelson HF Beebe Center for Scientific Computing,
math.utah.edu.
Paper [JP-1998-1]: On the Construction of the Osher-Solomon
Scheme for 3D Euler Equations
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M. Feistauer:
Analysis in compressible fluid mechanics,
ZAMM 78 (9): 579-596, 1998.
Citations and References to Software
XGEN: 2D Unstructured Mesh Generator
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S. Owen: A Survey of Unstructured Mesh Generation Technology,
7th International Meshing Roundtable, Sandia National Laboratories,
1998.
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S. Owen: Meshing Research Corner/Meshing Software Survey,
http://www.andrew.cmu.edu/user/sowen/softsurv.html.
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R. Schneiders: Mesh Generation & Grid Generation on the Web,
http://www-users.informatik.rwth-aachen.de/%7Eroberts/meshgeneration.html
EULER: Multi-Dimensional Finite Volume Solver for
Compressible Flow
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Free and Low-Cost CFD Software: Aerodynamics and Aerospace,
http://capella.colorado.edu/~laney/softaero.htm
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Roger Young and Ian MacPhedran:
IFER, Internet Finite Element Resourses/Finite Volume Methods,
http://www.engr.usask.ca/~macphed/finite/fe_resources/fe_resources.html
Master and Ph.D. theses based on my work
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Martin Zitka: Adaptive Higher-Order Finite Element Methods for
Elliptic Problems in 3D, Faculty of Mathematics and Physics, Dept.
of Numerical Mathematics, Charles University, Prague, 2008.
Advisor: Karel Segeth
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Petr Kubasek: Computational Comparison of hp-Adaptive Methods,
Faculty of Mathematics and Physics, Dept.
of Numerical Mathematics, Charles University, Prague, 2008.
Advisor: Tomas Vejchodsky
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M. Zoubek: Adaptive Methods for the Numerical Solution of
3D Compressible Euler Equations,
Master's Thesis, Faculty of Mathematics and Physics, Dept.
of Numerical Mathematics, Charles University, Prague, 2001.
Advisor: Jiri Felcman
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D. K. Datta: Computer Analysis of Error Estimation in Finite Element
Computations for Elliptic and Parabolic Problems, Ph.D. Thesis,
Texas A&M University, College Station, Texas, August 2001.
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D. Pardo: Integration of a Two-Grid Solver and Fully Automatic hp-Adaptivity,
Ph.D. Thesis, ICEM, The University of Texas at Austin, Texas, 2003.
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M. Zitka: Higher-Order Finite Element Method for Systems of
Nonlinear Parabolic Differential Equations,
Master's Thesis, Charles University, Faculty of Mathematics and Physics,
Prague, 2003.
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J. Rak: Analysis and Numerical Solution of a Second-Kind Fredholm Integral
Operator Related to Induction Heating,
Master's Thesis, Charles University, Faculty of Mathematics and Physics,
Prague, 2003.
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P. Tronner: Numerical Solution of Compressible Euler Equations by
the Finite Volume Method of Lines,
Master's Thesis, Czech Technical University, Faculty of
Mechanical Engineering, Brno, 2003.
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Hans Ginzel: Master's Thesis, Faculty of Mathematics and Physics, Dept.
of Numerical Mathematics, Charles University, Prague, 2003.
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J. Haskovec: Three-Dimensional Unstructured Parallel Grid Generator XGEN3D,
Master's Thesis, Faculty of Mathematics and Physics,
Charles University, Prague, 2003.