Numerical methods for automatic proof of the existence and the local uniqueness of weak solutions of elliptic boundary value problems with strongly nonlinear terms are proposed. They are based on the infinite dimensional fixed point theorems and the explicit error estimates for finite element approximations. We present detailed verification procedures and numerical examples for the typical model problem: — ∆u=eu.
ASJC Scopus subject areas
- Signal Processing
- Computer Science Applications
- Control and Optimization