Solution method for discrete double obstacle problems based on a power penalty approach

Abstract

<p style="text-indent:20px;">We develop a power penalty approach to a finite-dimensional double obstacle problem. This problem is first approximated by a system of nonlinear equations containing two penalty terms. We show that the solution to this penalized equation converges to that of the original obstacle problem at an exponential rate when the coefficient matrices are <inline-formula><tex-math id="M1">\begin{document}$ M $\end{document}</tex-math></inline-formula>-matrices. Numerical examples are presented to confirm the theoretical findings and illustrate the efficiency and effectiveness of the new method.</p>