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Variational Methods for Evolution
Oberwolfach Reports, 2012The meeting focused on the last advances in the applications of variational methods to evolution problems governed by partial differential equations. The talks covered a broad range of topics, including large deviation and variational principles, rate-independent evolutions and gradient flows, heat flows in metric-measure spaces, propagation of ...
Alexander Mielke+3 more
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1994
Publisher Summary This chapter focuses on the use of variational methods in the study of the energy methods of solid mechanics. The Galerkin method can be shown to produce element matrix integral definitions that would be identical to those obtained from a variational form, if one exists. Most nonlinear problems do not have a variational form, yet the
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Publisher Summary This chapter focuses on the use of variational methods in the study of the energy methods of solid mechanics. The Galerkin method can be shown to produce element matrix integral definitions that would be identical to those obtained from a variational form, if one exists. Most nonlinear problems do not have a variational form, yet the
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2004
In many cases stationary perturbation theory cannot be applied successfully as there may not be a closely related problem which is capable of exact solution.
S. Lokanathan, Ajoy Ghatak
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In many cases stationary perturbation theory cannot be applied successfully as there may not be a closely related problem which is capable of exact solution.
S. Lokanathan, Ajoy Ghatak
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Variational Methods of Approximation [PDF]
In this chapter, we describe several of the more popular variational methods for the approximate solution of boundary-and initial-value problems. For ease in presentation, we confine our attention to linear problems, and most of what we present has to do with elliptic boundary-value problems. In particular, we discuss interpolation properties of finite
J. N. Reddy, J. T. Oden
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The variational collocation method
Computer Methods in Applied Mechanics and Engineering, 2016We propose the variational collocation method for the numerical solution of partial differential equations. The conceptual basis is the establishment of a direct connection between the Galerkin method and the classical collocation methods, with the perspective of achieving the accuracy of the former with a computational cost of one point evaluation per
Hector Gomez, Laura De Lorenzis
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