A Quasi-Projection Analysis of Galerkin Methods for Parabolic and Hyperbolic Equations
نویسندگان
چکیده
منابع مشابه
A Quasi-Projection Analysis of Galerkin Methods for Parabolic and Hyperbolic Equations
Superconvergence phenomena are demonstrated for Galerkin approximations of solutions of second order parabolic and hyperbolic problems in a single space variable. An asymptotic expansion of the Galerkin solution is used to derive these results and, in addition, to show optimal order error estimates in Sobolev spaces of negative index in multiple dimensions.
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Henceforth, it will be assumed that (1.1) has a unique solution U. Precise hypotheses on the required smoothness of the solution will be made when needed. For s a nonnegative integer, let H” = H”(Q) be the Sobolev space W,“(R) of real-valued functions on R and let 11. /Is denote its usual norm. Let fi’ = ii’(Q) = {u E H’ :ulm = 0). Th e inner product on L* = L’(Q) is denoted by (. , .) and the ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1978
ISSN: 0025-5718
DOI: 10.2307/2006148