In this paper we investigate a semi-discrete H1 -Galerkin mixed finite element approximation of one kind of nolocal second order nonlinear hyperbolic equation, which is often used to describe vibration of an elastic string. A priori error estimates for the semi-discrete scheme are derived. A fully discrete scheme is constructed and one numerical example is given to verify the theoretical findings.
Chen, F., & Zhou, Z. (2017). An H1 -Galerkin Mixed Finite Element Approximation of a Nonlocal Hyperbolic Equation. Mathematical Modelling and Analysis, 22(5), 643-653. https://doi.org/10.3846/13926292.2017.1346524
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