The Variational Formulation of Elliptic PDEs

2016 ◽  
pp. 117-143
Author(s):  
Hervé Le Dret ◽  
Brigitte Lucquin
Keyword(s):  
Variational Formulation ◽  
Elliptic Pdes

scholarly journals A robust solver for elliptic PDEs in 3D complex geometries

2021 ◽  
pp. 110511
Author(s):  
Matthew J. Morse ◽  
Abtin Rahimian ◽  
Denis Zorin
Keyword(s):  
Elliptic Pdes ◽  
Complex Geometries

Two-grid IPDG discretization scheme for nonlinear elliptic PDEs

2020 ◽  
pp. 105587
Author(s):  
Liuqiang Zhong ◽  
Liangliang Zhou ◽  
Chunmei Liu ◽  
Jie Peng
Keyword(s):  
Elliptic Pdes ◽  
Discretization Scheme ◽  
Nonlinear Elliptic

scholarly journals Variational formulations of steady rotational equatorial waves

2020 ◽  
Vol 10 (1) ◽  
pp. 534-547
Author(s):  
Jifeng Chu ◽  
Joachim Escher
Keyword(s):  
Linear Stability ◽  
Stream Function ◽  
Water Waves ◽  
Variational Formulation ◽  
Energy Functional ◽  
Equatorial Waves ◽  
Second Variation ◽  
Governing Equations ◽  
The Second Variation ◽  
Variational Formulations

Abstract When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional 𝓗 in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.

A piezoelectric contact problem with slip dependent friction and damage

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Abderrezak Kasri
Keyword(s):  
Weak Solution ◽  
Contact Problem ◽  
Dry Friction ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Normal Compliance ◽  
Electrically Conductive ◽  
Coulomb’S Law ◽  
Electrical Condition ◽  
Coulomb's Law

Abstract The aim of this paper is to study a quasistatic contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The contact is modelled with an electrical condition, normal compliance and the associated version of Coulomb’s law of dry friction in which slip dependent friction is included. We derive a variational formulation for the model and, under a smallness assumption, we prove the existence and uniqueness of a weak solution.

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