Analytical and numerical solutions of a class of nonlinear integro-differential equations with L1 kernels. (February 2020) - Xu, Da
Abstract: We study the finite element approximations to a general class of nonlinear and nonlocal hyperbolic integro-differential equations with L 1 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 ∞ ( H 0 1 ( Ω ) ) -norms. For the completely discrete scheme, linearized backward Euler method is defined and error estimates in l ∞ ( H 0 1 ( Ω ) ) -norm are proved. Several numerical experiments are reported to confirm our theoretical findings.