  BDDC and FETI-DP algorithms are developed for three-dimensional elliptic
problems with adaptively enriched coarse components. It is known that these
enriched components are necessary in the development of robust preconditioners.
To form the adaptive coarse components, carefully designed generalized
eigenvalue problems are introduced for each faces and edges, and the coarse
components are formed by using eigenvectors with their corresponding
eigenvalues larger than a given tolerance $\lambda_{TOL}$. Upper bounds for
condition numbers of the preconditioned systems are shown to be $C
\lambda_{TOL}$, with the constant $C$ depending only on the maximum number of
edges and faces per subdomain, and the maximum number of subdomains sharing an
edge. Numerical results are presented to test the robustness of the proposed
approach.
