Numerical Methods for Nonlinear Partial Differential Equations

The book opens with an introduction, then lays its groundwork in two chapters on analytical background and on the finite element method for linear problems, followed by a chapter on general concepts for discretized problems. The middle section applies these tools to classical formulations, including the obstacle problem, the Allen-Cahn equation, harmonic maps and bending problems. The final section turns to extended formulations, covering nonconvexity and microstructure, free discontinuities and elastoplasticity. Supporting material includes auxiliary routines, a list of frequently used notation and an index.