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We study the numerical solution of a Cahn-Hilliard/Allen-Cahn system withstrong coupling through state and gradient dependent non-diagonal mobilitymatrices. A fully discrete approximation scheme in space and time is proposedwhich preserves the underlying gradient flow structure and leads to dissipationof the free-energy on the discrete level. Existence and uniqueness of thediscrete solution is established and relative energy estimates are used toprove optimal convergence rates in space and time under minimal smoothnessassumptions. Numerical tests are presented for illustration of the theoreticalresults and to demonstrate the viability of the proposed methods.

A second-order structure-preserving discretization for the Cahn-Hilliard/Allen-Cahn system with cross-kinetic coupling