基于M axwell模型的线性粘弹性波传导问题的半离散/全离散杂交应力有限元法  

SEMI-DISCRETE AND FULLY DISCRETE HYBRID STRESS FINITE ELEMENT METHODS FOR MAXWELL VISCOELASTIC MODEL OF WAVE PROPAGATION

作　　者：王少杰 谢小平[1] Wang Shaojie;Xie Xiaoping(School of Mathematics,Sichuan University,Chengdu 610064)

机构地区：[1]四川大学数学学院,成都610064

出　　处：《高等学校计算数学学报》2021年第1期28-58,共31页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(11771312).

摘　　要：1引言设ΩСR^(2)为一个凸的有界开集,边界为ЭΩ;T为一个正常数.我们考虑如下基于Maxwell模型的二维粘弹性固体介质波传导问题。This paper proposes semi-discrete and fully discrete hybrid stress finite element methods for Maxwell-model-based problems of wave propagation in 2-dimensional linear viscoelastic solid.In the semi-discrete and fully discrete schemes,a 4-node hybrid stress quadrilateral finite element is used for the spatial discretization.In the fully discrete scheme,implicit differences of second order accuracy are used for the discretization of the temporal derivatives of displacement and stress.We prove the existence and uniqueness of the solutions of the semi-discrete scheme and fully discrete scheme,and derive their error estimates.We also obtain an unconditional stability result for the fully discrete scheme.Finally,numerical experiments are done to verify the theoretical results.

关 键 词：有界开集 杂交应力有限元 Maxwell模型 半离散 全离散 固体介质 线性粘弹性 传导 

分 类 号：O241.1[理学—计算数学] O242.21[理学—数学]