Unconditionally Stable Explicit Methods for Parabolic Equations.
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Uniform stabilization of a viscous numerical approximation for a locally damped wave equation
Arnaud Münch, Ademir Fernando Pazoto (2007)
ESAIM: Control, Optimisation and Calculus of Variations
This work is devoted to the analysis of a viscous finite-difference space semi-discretization of a locally damped wave equation in a regular 2-D domain. The damping term is supported in a suitable subset of the domain, so that the energy of solutions of the damped continuous wave equation decays exponentially to zero as time goes to infinity. Using discrete multiplier techniques, we prove that adding a suitable vanishing numerical viscosity term leads to a uniform (with respect to the mesh size)...
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