UNIFORM EXPONENTIAL DECAY IN THE TEMPORARY VARIABLE SEMI-DISCRETIZATION SPACE OF A DAMPED WAVE EQUATION - Gavilán Gonzales, Maruja (2011)
Our purpose is to analyze and to attain result in the classical numerical approximation schemes of the damped wave equation one-dimentional, with relation to exponential decay property of solutions and whether it is uniform with respect to the mesh size. We consider the finite-difference space semi-discretization of a locally damped wave equation. The decay rate of the semi-discrete systems turns out depend on the mesh size h goes to zero. We prove that adding a suitable vanishing numerical viscosity term leads to a uniform exponential decay of the energy of solutions.