Semi-discrete finite-element approximation of nonlocal hyperbolic problem

ABSTRACT

In this paper, we investigate a semi-discrete finite-element approximation of nonlocal hyperbolic problem. A priori error estimate for the semi-discrete scheme is derived. A fully discrete scheme based on backward difference method is constructed. We discuss the existence-uniqueness of the solution for fully discrete problem. In order to linearize the nonlinear fully discrete problem, we use Newton's method. Numerical results based on the usual finite-element method are provided to confirm the theoretical estimate.

KEYWORDS:

• Nonlocal hyperbolic problem
• finite-element method
• backward difference method
• newton iteration method

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65N12
• 65N15
• 65N22
• 35N30

Disclosure statement

No potential conflict of interest was reported by the authors.