فضه برزگر

This thesis presents a method for numerically solving linear time-dependent partial differential equations. It combines the finite element method with a spectral approach using Gauss-Legendre-Lobatto points. In the temporal dimension, the Crank-Nicolson method is employed due to its prominent features, such as unconditional stability an‎d second-order accuracy, which have been proven. The Gauss-Legendre-Lobatto points are used as interpolation nodes in spectral elements an‎d as quadrature points for numerical integration. One of the most significant an‎d widely applicable problems in time-dependent PDEs is the viscoelastic wave propagation model, which plays a crucial role in seismic wave modeling. The numerical solution of the viscoelastic wave equation using the spectral element method presents notable challenges in error analysis. In this research, the convergence rates for both the semi-discrete time scheme an‎d the fully discrete space-time scheme are analyzed an‎d determined. Numerical results obtained from the viscoelastic wave model demonstrate the high accuracy an‎d potential capability of the proposed method, highlighting its applicability as an efficient an‎d powerful technique for solving complex time-dependent PDEs.

معادلات موج ويسكوالاستيك , روش المان‌ طيفي , نقاط گاوس لژاندر لوباتو , تحليل خطا

Viscoelastic wave equations , Spectral element method , Gauss-Legendre-Lobatto points , Error analysis.

Baregar

Dr, Rashidinia