A mixed finite element method for nonlinear elasticity: two-fold saddle point approach and a-posteriori error estimate

2002 ◽  
Vol 91 (2) ◽  
pp. 197-222 ◽  
Author(s):  
Mauricio A. Barrientos ◽  
Gabriel N. Gatica ◽  
Ernst P. Stephan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimate ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Posteriori Error ◽  
A Posteriori Error Estimate ◽  
Posteriori Error Estimate ◽  
A Posteriori ◽  
A Posteriori Error

scholarly journals An adaptive finite element DtN method for the elastic wave scattering by biperiodic structures

2021 ◽  
Author(s):  
Gang Bao ◽  
Xue Jiang ◽  
Peijun Li ◽  
Xiaokai Yuan
Keyword(s):  
Finite Element ◽  
Error Estimate ◽  
Elastic Wave ◽  
Posteriori Error ◽  
A Posteriori Error Estimate ◽  
Posteriori Error Estimate ◽  
Adaptive Finite Element ◽  
A Posteriori ◽  
Truncation Parameter ◽  
A Posteriori Error

Consider the scattering of a time-harmonic elastic plane wave by a bi-periodic rigid surface. The displacement of elastic wave motion is modeled by the three-dimensional Navier equation in an unbounded domain above the surface. Based on the Dirichlet-to-Neumann (DtN) operator, which is given as an infinite series, an exact transparent boundary condition is introduced and the scattering problem is formulated equivalently into a boundary value problem in a bounded domain. An a posteriori error estimate based adaptive finite element DtN method is proposed to solve the discrete variational problem where the DtN operator is truncated into a finite number of terms. The a posteriori error estimate takes account of the finite element approximation error and the truncation error of the DtN operator which is shown to decay exponentially with respect to the truncation parameter. Numerical experiments are presented to illustrate the effectiveness of the proposed method.

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