scholarly journals A Study on Moving Mesh Finite Element Solution of Phase-Field Models for Hydraulic Fracturing

2018 ◽  
Vol 9 (2) ◽  
pp. 51-57
Author(s):  
Fei Zhang ◽  
◽  
Shicheng Zhang ◽  
Weizhang Huang ◽  
Xianping Li ◽  
...  
Keyword(s):  
Finite Element ◽  
Hydraulic Fracturing ◽  
Phase Field ◽  
Finite Element Solution ◽  
Moving Mesh ◽  
Element Solution ◽  
Phase Field Models

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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