Some remarks on the Galerkin approximation of parabolic equations
H. Marcinkowska, A. Szustalewicz (1988)
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Some remarks on the Galerkin approximation of parabolic equations
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In this paper, the author introduces parabolic generalized local Morrey spaces and gets the boundedness of a large class of parabolic rough operators on them. The author also establishes the parabolic local Campanato space estimates for their commutators on parabolic generalized local Morrey spaces. As its special cases, the corresponding results of parabolic sublinear operators with rough kernel and their commutators can be deduced, respectively. At last, parabolic Marcinkiewicz operator...
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We consider discontinuous as well as continuous Galerkin methods for the time discretization of a class of nonlinear parabolic equations. We show existence and local uniqueness and derive optimal order optimal regularity error estimates. We establish the results in an abstract Hilbert space setting and apply them to a quasilinear parabolic equation.