From Euler, Ritz, and Galerkin to Modern Computing
نویسندگان
چکیده
منابع مشابه
From Euler, Ritz, and Galerkin to Modern Computing
The so-called Ritz–Galerkin method is one of the most fundamental tools of modern computing. Its origins lie in Hilbert’s “direct” approach to the variational calculus of Euler– Lagrange and in the thesis of Walther Ritz, who died 100 years ago at the age of 31 after a long battle with tuberculosis. The thesis was submitted in 1902 in Göttingen, during a period of dramatic developments in physi...
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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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Existence, uniqueness and error estimates for Ritz-Galerkin methods are o discussed in the case where the associated bilinear form satisfies a Carding type inequality, i.e., it is indefinite in a certain way. An application to the finite element method is given. In this note, we would like to discuss existence, uniqueness and estimates over the whole domain for some Ritz-Galerkin methods where ...
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— This paper describes a gênerai formulation of the Euler Characteristic Galerkin (ECG) scheme for scalar conservation laws, based on the theory of the Riemann-Stieltjes intégral. The ECG scheme is proved to be equivalent to the projection of Brenier' s transportcollapse operator. For the purpose of getting higher order accuracy, we explore two recovery procedures, namely continuous linear reco...
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ژورنال
عنوان ژورنال: SIAM Review
سال: 2012
ISSN: 0036-1445,1095-7200
DOI: 10.1137/100804036