The Crank–Nicolson finite element method for the 2D uniform transmission line equation

Abstract

Abstract We develop the Crank–Nicolson finite element (CNFE) method for the two-dimensional (2D) uniform transmission line equation, study the stability and existence as well as error estimates for the CNFE solutions of the 2D uniform transmission line equation by strict theoretical approaches. We verify the correctness of the obtained theoretical results by means of numerical tests.

Keywords

• Crank–Nicolson finite element method
• Uniform transmission line equation
• Stability and existence
• Error estimate
• Numerical test