We propose and analyze an HDG scheme for the Laplace-domain interaction between a transient acoustic wave and a bounded elastic solid embedded in an unbounded fluid medium. Two mixed variables (the stress tensor and the velocity of the acoustic wave) are included while the symmetry of the stress tensor is imposed weakly by considering the antisymmetric part of the strain tensor (the spin or vorticity tensor) as an additional unknown. Convergence of the method is demonstrated and theoretical rates are obtained; numerical results suggesting optimal order of convergence and superconvergence of the traces are presented.

翻译：本文提出并分析了一种用于瞬态声波与嵌入无限流体介质中的有界弹性固体之间拉普拉斯域相互作用的HDG方案。该方案包含两个混合变量（应力张量和声波速度），同时通过将应变张量的反对称部分（自旋或涡量张量）作为附加未知量，以弱形式施加应力张量的对称性。我们证明了该方法的收敛性并获得了理论收敛阶；数值结果表明该方法具有最优收敛阶以及迹的超收敛特性。