A Two-Level Additive Schwarz Preconditioner for C0 Interior Penalty Methods for Cahn-Hilliard Equations
We study a two-level additive Schwarz preconditioner for C 0 interior penalty methods for a biharmonic problem with essential and natural boundary conditions with Cahn-Hilliard type. We show that the condition number of the preconditioned system is bounded by C(1 + (H 3 ∕ δ 3)), where H is the typical diameter of a subdomain, δ measures the overlap among the subdomains, and the positive constant C is independent of the mesh sizes and the number of subdomains.
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