A C0 interior penalty discontinuous Galerkin Method for fourth‐order total variation flow. II: Existence and uniqueness. Issue 4 (25th February 2019)

• Record Type: Journal Article
• Authors: Bhandari, Chandi; Hoppe, Ronald H.W.; Kumar, Rahul
• Is Part Of: Numerical methods for partial differential equations. Volume 35:Issue 4(2019)
• Page Start: 1477
• Page End: 1496
• Publication Date: 2019-02-25
• Subjects: C0 interior penalty discontinuous Galerkin method -- existence and uniqueness -- fourth‐order total variation flow; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22365
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : We prove the existence and uniqueness of a solution of a C 0 Interior Penalty Discontinuous Galerkin (C 0 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 C 0 IPDG approximation is Lipschitz continuous and strongly monotone on bounded sets of the underlying finite element space.