Abstract
A numerical technique which enables us to verify the existence of weak solutions for nonlinear elliptic boundary value problems is proposed. It is based on the infinite dimensional fixed point theorems using the Newton-like operator and the error estimates for finite element approximations. We also present an effective verification procedure which automatically generates the set including the exact solution in a computer. Some numerical examples are illustrated.
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Watanabe, Y., Nakao, M.T. Numerical verifications of solutions for nonlinear elliptic equations. Japan J. Indust. Appl. Math. 10, 165–178 (1993). https://doi.org/10.1007/BF03167208
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DOI: https://doi.org/10.1007/BF03167208