Multiple-grid finite element solution of the shallow water equations: Water hammer phenomenon

2014 ◽  
Vol 90 ◽  
pp. 65-71 ◽  
Author(s):  
A. Triki
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Hammer ◽  
Finite Element Solution ◽  
Element Solution

scholarly journals Robust Iterative Solvers for Gao Type Nonlinear Beam Models in Elasticity

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. Borsos ◽  
János Karátson
Keyword(s):  
Finite Element ◽  
Newton Method ◽  
Newton's Method ◽  
Numerical Experiments ◽  
Elliptic Problems ◽  
Iterative Solvers ◽  
Finite Element Solution ◽  
Element Solution ◽  
Nonlinear Beam ◽  
Quasi Newton

Abstract The goal of this paper is to present various types of iterative solvers: gradient iteration, Newton’s method and a quasi-Newton method, for the finite element solution of elliptic problems arising in Gao type beam models (a geometrical type of nonlinearity, with respect to the Euler–Bernoulli hypothesis). Robust behaviour, i.e., convergence independently of the mesh parameters, is proved for these methods, and they are also tested with numerical experiments.

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