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Keyword

variational formulation

Description: A variational formulation expresses a mathematical or physical problem through integral principles or functionals, often enabling analytical and numerical solution.
OpenAlex ID: keywords/weak-formulation
The Finite Element Method: its Basis and Fundamentals
2013 · Zienkiewicz, Olgierd C. 1921-2009, Taylor, Robert L. 1934-, et al. · Elsevier eBooks · 3,479
Thermoelasticity and Irreversible Thermodynamics
1956 · M. A. Biot · Journal of Applied Physics · 3,164
Mixed and Hybrid Finite Element Methods
2011 · Franco Brezzi, Michel Fortin · CERN Document Server (European Organization for Nuclear Research) · 2,401
Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications
2009 · F. Roters, P. Eisenlohr, et al. · Acta Materialia · 2,181
Dynamics of Structures
1977 · Ray W. Clough, Joseph Penzien, et al. · Journal of Applied Mechanics · 1,922
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Numerical approximation of partial differential equations
1987 · Quarteroni, Alfio 1952-, Valli, Alberto · Mathematics and Computers in Simulation · 1,864
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Level Set Evolution without Re-Initialization: A New Variational Formulation
2005 · Chunming Li, Chenyang Xu, et al. · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · 1,813
Numerical Methods for Nonlinear Variational Problems
1984 · Roland Glowinski · Springer eBooks · 1,745
A three-dimensional finite-strain rod model. part II: Computational aspects
1986 · J.C. Simo, L. Vu-Quoc · Computer Methods in Applied Mechanics and Engineering · 1,215
Bernoulli–Euler beam model based on a modified couple stress theory
2006 · S K Park, X-L Gao · Journal of Micromechanics and Microengineering · 1,099
A Variational Level Set Approach to Multiphase Motion
1996 · Hong-Kai Zhao, T. Chan, et al. · Journal of Computational Physics · 1,060
Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
2010 · Jie Shen, Xiaofeng Yang · Discrete and Continuous Dynamical Systems · 995
A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites
1996 · W.J. Drugan, J.R. Willis · Journal of the Mechanics and Physics of Solids · 969
Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics.
1992 · J. Tinsley Oden, Roland Glowinski, et al. · Mathematics of Computation · 959
Variational and momentum preservation aspects of Smooth Particle Hydrodynamic formulations
1999 · J. Bonet, T.-S.L. Lok · Computer Methods in Applied Mechanics and Engineering · 833
hp-VPINNs: Variational physics-informed neural networks with domain decomposition
2020 · Ehsan Kharazmi, Zhongqiang Zhang, et al. · Computer Methods in Applied Mechanics and Engineering · 823
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Data-driven computational mechanics
2016 · T. Kirchdoerfer, M. Ortiz · Computer Methods in Applied Mechanics and Engineering · 815
Boundary Element Methods
1981 · Brebbia, Carlos · Springer eBooks · 789
Variational formulation for the stationary fractional advection dispersion equation
2005 · Vincent J. Ervin, John Paul Roop · Numerical Methods for Partial Differential Equations · 763
DOLFIN
2010 · Anders Logg, Garth N. Wells · ACM Transactions on Mathematical Software · 750
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Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities
2003 · P. Sharma, S. Ganti, et al. · Applied Physics Letters · 742
Diffraction Theory
1954 · C J Bouwkamp · Reports on Progress in Physics · 719
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The Generalized Interpolation Material Point Method
2004 · Scott Bardenhagen, Edward M. Kober · Computer Modeling in Engineering & Sciences · 672
Unified form language
2014 · Martin S. Alnæs, Anders Logg, et al. · ACM Transactions on Mathematical Software · 633
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A generalized field method for multiphase transformations using interface fields
1999 · I. Steinbach, F. Pezzolla · Physica D Nonlinear Phenomena · 605
Works count: 10,970
Citation count: 184,100
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