Premium
A C 0 interior penalty discontinuous Galerkin Method for fourth‐order total variation flow. II: Existence and uniqueness
Author(s) -
Bhandari Chandi,
Hoppe Ronald H.W.,
Kumar Rahul
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22365
Subject(s) - mathematics , uniqueness , lipschitz continuity , discontinuous galerkin method , monotone polygon , mathematical analysis , nonlinear system , finite element method , space (punctuation) , weak solution , bounded function , galerkin method , bounded variation , order (exchange) , lemma (botany) , operator (biology) , flow (mathematics) , geometry , philosophy , repressor , ecology , linguistics , chemistry , biology , biochemistry , quantum mechanics , transcription factor , thermodynamics , physics , poaceae , finance , economics , gene
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.