Continuous Petrov-Galerkin methods for nonlinear problems

This thesis investigates continuous Petrov-Galerkin methods for nonlinear initial value problems. An existence and uniqueness proof from the literature is given in a simplified version. Existing arguments to prove convergence are reformulated into consistency and stability results, which are then combined to give an alternative proof of convergence. Results regarding the energy consistency are collected. Challenges in the numerical implementation are discussed. An implementation in Matlab is used to confirm theoretical results and to compare two methods to solve the arising nonlinear system.