Guaranteed lower bounds of the smallest eigenvalues of elliptic differential operators (Q2874285)

The authors are concerned with a method for sharp estimation of the lower bounds of the smallest eigenvalue of divergence type elliptic operators. They are supplied with mixed or purely von Neumann boundary conditions. The method is a domain decomposition one. The domain splits into some overlapping subdomains such that on each of them the estimates of the minimal positive eigenvalue are fairly rigorously computable. Therefore, the problem is reduced to a finite-dimensional variational one. Its dimension depends on the number of subdomains. The minimization functionals depend on the topological structure of the overlapping subdomains. Some numerical experiments are carried out in order to show the accuracy of the estimates.