Numerical approximations for damped wave equation with Neumann boundary conditions

This research paper investigates the numerical analysis of the damped wave equation (DWE), focusing on the properties of numerical solutions achieved via semi-discrete approximation (SDA) and fully-discrete approximation (FDA) finite element methods (FEMs). This study established the existence of SDA and FDA solutions. Theoretical results are validated with numerical examples conducted in one, two, and three dimensions, demonstrating the accuracy and effectiveness of the proposed approaches.