A C0 interior penalty discontinuous Galerkin Method for fourth‐order total variation flow. II: Existence and uniqueness

We prove the existence and uniqueness of a solution of a C⁰ Interior Penalty Discontinuous Galerkin (C⁰ IPDG) method for the numerical solution of a fourth‐order total variation flow problem that has been developed in part I of the paper. The proof relies on a nonlinear version of the Lax‐Milgram Lemma. It requires to establish that the nonlinear operator associated with the C⁰ IPDG approximation is Lipschitz continuous and strongly monotone on bounded sets of the underlying finite element space.