Yoshitaka Watanabe, Nobito Yamamoto and Mitsuhiro T. Nakao:

Verified Computations of Solutions for Nondifferentiable Elliptic
Equations Related to MHD Equilibria,

*Nonlinear Analysis, Theory, Methods & Applications*,
Vol.28, No.3 (1997) pp.577-587.

This paper proposes a numerical technique to enclose the exact solution with
guaranteed error bounds for nondifferentiable nonlinear elliptic
equations of second order related to MHD equilibria.
This method is a kind of Newton-like method using an enclosing technique
combined with the explicit error estimate for finite element approximations.

Construct a concrete computing algorithm for the verification in computer,
which is an efficient computing algorithm from the view point of
interval arithmetic, and some numerical examples are presented.
10pages.

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