Abstract
We study the finite element approximations to a general class of nonlinear and nonlocal hyperbolic integro-differential equations with L1 convolution kernels. The continuous time Galerkin procedures are defined and global existence of a unique discrete solution is derived. Moreover, optimal error estimates are shown in the L∞(H01(Ω))-norms. For the completely discrete scheme, linearized backward Euler method is defined and error estimates in l∞(H01(Ω))-norm are proved. Several numerical experiments are reported to confirm our theoretical findings.
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