Interior estimates for Ritz-Galerkin methods
نویسندگان
چکیده
منابع مشابه
Interior Estimates for Ritz - Galerkin Methods
Interior a priori error estimates in Sobolev norms are derived from interior RitzGalerkin equations which are common to a class of methods used in approximating solutions of second order elliptic boundary value problems. The estimates are valid for a large class of piecewise polynomial subspaces used in practice, which are defined on both uniform and nonuniform meshes. It is shown that the erro...
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In this paper we obtain, by simple means, interior maximum-norm estimates for a class of Ritz-Galerkin methods used for approximating solutions of second order elliptic boundary value problems in R . The estimates are proved when the approximating subspaces are any of a large class of piecewise polynomial subspaces which we assume here to be defined on a uniform mesh on the interior domain. Opt...
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New uniform error estimates are established for finite element approximations uh of solutions u of second-order elliptic equations Lu = f using only the regularity assumption ‖u‖1 ≤ c‖f‖−1. Using an Aubin–Nitsche type duality argument we show for example that, for arbitrary (fixed) ε sufficiently small, there exists an h0 such that for 0 < h < h0 ‖u− uh‖0 ≤ ε‖u− uh‖1. Here, ‖ · ‖s denotes the n...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1974
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1974-0373325-9