Space-Time Finite Element Methods for Parabolic Evolution Problems with Variable Coefficients

2019 ◽  
pp. 247-275 ◽  
Author(s):  
Ulrich Langer ◽  
Martin Neumüller ◽  
Andreas Schafelner
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Variable Coefficients ◽  
Space Time ◽  
Evolution Problems

Unified Space–Time Finite Element Methods for Dissipative Continua Dynamics

2017 ◽  
Vol 09 (02) ◽  
pp. 1750019 ◽  
Author(s):  
Jinkyu Kim ◽  
Gary F. Dargush ◽  
Hwasung Roh ◽  
Jaeho Ryu ◽  
Dongkeon Kim
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Analytical Investigation ◽  
Space Time ◽  
Time Step ◽  
Average Acceleration ◽  
Acceleration Method ◽  
Step Algorithm ◽  
Displacement Based ◽  
Continuum Dynamics

Based upon the extended framework of Hamilton’s principle, unified space–time finite element methods for viscoelastic and viscoplastic continuum dynamics are presented, respectively. For numerical efficiency, mixed time-step algorithm in time- and displacement-based algorithm in space are adopted. Through analytical investigation, we demonstrate that the Newmark’s constant average acceleration method and the present method are the same for viscoelasticity. With spatial eight-node brick elements, some numerical simulations are undertaken to validate and investigate the performance of the present non-iterative space–time finite element method for viscoplasticity.

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