Computer-assisted analysis of the sign-change structure for elliptic problems
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In this paper, a method is proposed for rigorously analyzing the sign-change structure of solutions to elliptic problems with computer-assistance. Suppose that errors u-û_H^1_0 and u-û_L^∞ are evaluated between an exact solution u and a numerically computed approximate solution û. We estimate the number of sign-changes of the solution u (the number of nodal domains) and the location of zero level-sets of u (the location of the nodal line). We present numerical examples where our method is applied to a specific semilinear elliptic problem.
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