An H¹-Galerkin Mixed Finite Element Approximation of a Nonlocal Hyperbolic Equation

Abstract

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.

Keywords:

• nonlocal hyperbolic equation
• H¹-Galerkin mixed finite element method
• a priori error estimate

AMS Subject Classification:

• 65N30