Splitting positive definite mixed element method for viscoelasticity wave equation

Yang LIU, Hong LI, Wei GAO, Siriguleng HE, Jinfeng WANG

Front. Math. China ›› 2012, Vol. 7 ›› Issue (4) : 725-742.

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PDF(463 KB)
Front. Math. China ›› 2012, Vol. 7 ›› Issue (4) : 725-742. DOI: 10.1007/s11464-012-0183-8
RESEARCH ARTICLE
RESEARCH ARTICLE

Splitting positive definite mixed element method for viscoelasticity wave equation

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Abstract

A splitting positive definite mixed finite element method is proposed for second-order viscoelasticity wave equation. The proposed procedure can be split into three independent symmetric positive definite integro-differential sub-system and does not need to solve a coupled system of equations. Error estimates are derived for both semidiscrete and fully discrete schemes. The existence and uniqueness for semidiscrete scheme are proved. Finally, a numerical example is provided to illustrate the efficiency of the method.

Keywords

Viscoelasticity wave equation / transformation / splitting positive definite system / mixed finite element method / error estimate

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Yang LIU, Hong LI, Wei GAO, Siriguleng HE, Jinfeng WANG. Splitting positive definite mixed element method for viscoelasticity wave equation. Front Math Chin, 2012, 7(4): 725‒742 https://doi.org/10.1007/s11464-012-0183-8

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