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On Convergence of Semidiscrete Ritz‐Galerkin Schemes Applied to the Boundary Control of Parabolic Equations with Non‐Linear Boundary Condition
Author(s) -
Tröltzsch F.
Publication year - 1992
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19920720712
Subject(s) - mathematics , galerkin method , boundary value problem , mathematical analysis , boundary (topology) , convergence (economics) , ritz method , semigroup , mixed boundary condition , finite element method , physics , economics , thermodynamics , economic growth
The paper is concerned with Ritz‐Galerkin approximations of parabolic control problems, where the control is acting in a non‐linear boundary condition. At first the convergence of the Ritz‐Galerkin method for parabolic initial‐boundary value problems with non‐linear boundary condition containing “rough” boundary data is proved by semigroup techniques. Then this result is applied to show convergence of optimal values for approximated control problems.