ε ∂2u

Summary. The main goal of this paper is to address the numerical solution of a wave equation with discontinuous coefficients by a finite element method using domain decomposition and semimatching grids. A wave equation with absorbing boundary conditions is considered, the coefficients in the equation essentially dif-fer in the subdomains. The problem is approximated by an explicit in time finite difference scheme combined with a piecewise linear finite element method in the space variables on a semimatching grid. The matching condition on the interface is taken into account by means of Lagrange multipliers. The resulting system of linear equations of the saddle-point form is solved by a conjugate gradient method. 1 Formulation of the problem Let Ω ⊂ R2 be a rectangular domain with sides parallel to the coordinate axes and boundary Γext (see Fig. 1). Now let Ω2 ⊂ Ω be a proper subdomain of Ω with a curvilinear boundary and Ω1 = Ω \ Ω̄2. We consider the following linear wave problem