On the Convergence of Ritz-Galerkin's Method | Zendy

Tetsuhiko Miyoshi | Zendy

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On the Convergence of Ritz-Galerkin's Method

Author(s) -

Tetsuhiko Miyoshi

Publication year - 1968

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195195265

Subject(s) - mathematics , galerkin method , boundary value problem , mathematical analysis , domain (mathematical analysis) , bounded function , ritz method , boundary (topology) , convergence (economics) , homogeneous , space (punctuation) , function (biology) , finite element method , combinatorics , economics , economic growth , linguistics , philosophy , physics , evolutionary biology , biology , thermodynamics

where D is a bounded domain in the (#, jO -plane, P is the boundary of D, and 0), &(:>0), c(>0), / are smooth functions defined on D. In Ritz-Galerkin's method, first we choose a system of linearly independent functions {^J such that they satisfy the given homogeneous boundary condition and they are dense in a function space containing the exact solution of the above boundary value problem, and next we seek the m-th approximation um in the form

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