**2. Viscous shallow-water equations**

The tsunami generated by the GEJE caused serious damage to the coastal areas of the Tohoku district. Numerical simulations are used to predict damage caused by tsunamis. Shallow-water equations are generally used in numerical simulations of tsunami propagation from the open sea to the coast. This subsection focuses on viscous shallow-water equations and attempts to generate a computational method using finite-element techniques based on the previous investigations of Kanayama and Ohtsuka [8].

In the numerical analysis of tsunami, a viscosity term is often omitted or simply added [6, 7]. In this subsection, however, a computational method that does not omit the viscosity term is adopted, that is, because it enables more rigorous analysis to be performed, and the authors intend to include the viscosity term in future stress analysis of tsunami. Recently, the authors have found an interesting book [10] that deals with sound mathematical topics related to the viscous shallow-water equations.
