Semi-discrete and Fully Discrete Finite-Element Methods with Penalty for the Numerical Solution of the Waterhammer Problem

1981 ◽  
Vol 18 (1) ◽  
pp. 111-128
Author(s):  
Nabil R. Nassif ◽  
Fabrice Pini
Keyword(s):  
Finite Element ◽  
Numerical Solution ◽  
Finite Element Methods ◽  
Fully Discrete ◽  
Discrete Finite Element

scholarly journals Fully Discrete Finite Element Methods for Two-Dimensional Bingham Flows

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Cheng Fang ◽  
Yuan Li
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Piecewise Linear ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Two Dimensional ◽  
Stabilized Finite Element ◽  
Fully Discrete ◽  
Stabilized Finite Element Method ◽  
Discrete Finite Element

This paper presents fully discrete stabilized finite element methods for two-dimensional Bingham fluid flow based on the method of regularization. Motivated by the Brezzi-Pitkäranta stabilized finite element method, the equal-order piecewise linear finite element approximation is used for both the velocity and the pressure. Based on Euler semi-implicit scheme, a fully discrete scheme is introduced. It is shown that the proposed fully discrete stabilized finite element scheme results in the h1/2 error order for the velocity in the discrete norms corresponding to L2(0,T;H1(Ω)2)∩L∞(0,T;L2(Ω)2).

Semi-Discrete and Fully Discrete Hybrid Stress Finite Element Methods for Elastodynamic Problems

2015 ◽  
Vol 8 (4) ◽  
pp. 582-604
Author(s):  
Zhengqin Yu ◽  
Xiaoping Xie
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Stability Result ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Quadrilateral Finite Element ◽  
Hybrid Stress Finite Element ◽  
Hybrid Stress

AbstractThis paper proposes and analyzes semi-discrete and fully discrete hybrid stress finite element methods for elastodynamic problems. A hybrid stress quadrilateral finite element approximation is used in the space directions. A second-order center difference is adopted in the time direction for the fully discrete scheme. Error estimates of the two schemes, as well as a stability result for the fully discrete scheme, are derived. Numerical experiments are done to verify the theoretical results.

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