A C 0 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 Le...

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Autores: Kumar, R.; Hoppe, R.H.W.; Bhandari, C.
Tipo de documento: Artículo
Estado:Accepted version
Fecha de publicación:2019
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/959
Acceso en línea:http://hdl.handle.net/20.500.11824/959
Nivel de acceso:Acceso abierto
Palabra clave:IPDG
Sumario: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.

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