NonconformingH1-Galerkin Mixed Finite Element Method for Strongly Damped Wave Equations

2013 ◽  
Vol 34 (12) ◽  
pp. 1348-1369 ◽  
Author(s):  
Dong-yang Shi ◽  
Qi-li Tang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equations ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Strongly Damped ◽  
Element Method

Asymptotic Expansions and Extrapolations of H1-Galerkin Mixed Finite Element Method for Strongly Damped Wave Equation

2015 ◽  
Vol 7 (5) ◽  
pp. 610-624 ◽  
Author(s):  
Dongyang Shi ◽  
Qili Tang ◽  
Xin Liao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equation ◽  
Convergence Rates ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Damped Wave Equation ◽  
Strongly Damped Wave Equation ◽  
Strongly Damped ◽  
Element Method

AbstractIn this paper, a high-accuracy H1-Galerkin mixed finite element method (MFEM) for strongly damped wave equation is studied by linear triangular finite element. By constructing a suitable extrapolation scheme, the convergence rates can be improved from 𝒪(h) to 𝒪(h3) both for the original variable u in H1(Ω) norm and for the actual stress variable p = ∇ut in H(div;Ω) norm, respectively. Finally, numerical results are presented to confirm the validity of the theoretical analysis and excellent performance of the proposed method.

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