Nonconforming finite element methods for the simulation of waves in viscoelastic solids Original Research Article

The propagation of waves in two- and three-dimensional bounded viscoelastic media is described in the space–frequency domain, leading to a Helmholtz-type boundary value problem, which is noncoercive, non-Hermitian, and complex valued. First-order absorbing boundary conditions are derived and used to minimize spurious reflections from the artificial boundaries. The paper consists of two parts. In Part I we describe the global procedures for the approximate solution of the problem. Simplicial and rectangular nonconforming finite element methods are employed for the spatial discretization. Optimal error estimate in a broken energy and L2(Ω) norms are derived using a bootstrapping argument of Schatz. Also a hybridization of these procedures is analyzed. In Part II we define and analyze nonoverlapping domain decomposition iterative methods. Convergence results are derived and numerical experiments showing the potential applicability in seismology are presented.