Abstract
In this paper, we propose a finite element method for solving viscoelastic hyperbolic integrodifferential equations with L1 kernel, involving a nonlocal and nonlinear damped coefficient. Firstly, we discuss and deduce that the L1 kernel is of positive type in two cases. Subsequently, based on the continuous Galerkin technique and the energy argument, we prove the global existence and uniqueness of the discrete solution. Finally, using the basic properties of the positive-type kernel, we derive the error estimates of the finite element solutions.
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