C~0-continuous Time Stepping Linear Finite Element Method: Theory And Algorithms

This thesis proposes a C~0-continuous time stepping linear finite element methodto solve initial-value problems for the second order scalar linear ordinary differentialequation. Some error results are proved by the direct computation. The numericalresults coincide with the theoretical estimates. Furthermore, this method was extendedto linear wave equations in two dimension, and some numerical tests are included toshow the computational performance of the method.