This is based on chapters from The Finite Element Method: Theory, Implementation, and Applications by Mats G. Larson and Fredrik Bengzon. Some solvers are made with Python, MATLAB, or both. My goal is ...

To derive Newton's method, it is convenient to start with a Taylor series expansion of the residual function: $$ R(u_i) = R(u_{i-1}) + \frac{\partial \textbf{R ...