A model of rupturing lithospheric faults with reoccurring earthquakes (Q2862274)

In this paper a litospheric model for equarthquakes is considered from the mathematical point of view. The authors use an isothermal small-strain model that combines the Maxwell-rheology, damage modelling and perfect plasticity in bulk. Thus the mathematical model can describe propagation of rupters of the fault zone as well as weakening/healing processes. Moreover, the model also covers the emission of seismic waves, propagation of sudden rupters of the fault and fluid-like aseismic response between ruptures. The authors analyse rigorously the above model and provide a numerical scheme that can be analysed from the numerical point of view with respect to its stability and convergence. They accompany a generic model of the bulk material, based on specification of appropriate storage energy and dissipation potentials, with a certain variantional principle. This allows to decrsibe fully reversible as well as irreversible components of the energy and material evolution. They derive a weak formulation of the model and show the existence of the so-called energetic weak solutions. The convergence of semi-implicit approximations is shown assuming damage-independent viscous attenuation. Numerical experiments presented at the end of paper confirm convergence and stability of the proposed scheme.