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Optimal error estimate and superconvergence of the DG method for first-order hyperbolic problems

✍ Scribed by Tie Zhang; Zheng Li

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
352 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

We consider the original discontinuous Galerkin method for the first-order hyperbolic problems in d-dimensional space. We show that, when the method uses polynomials of degree k, the L 2 -error estimate is of order k + 1 provided the triangulation is made of rectangular elements satisfying certain conditions. Further, we show the O(h 2k+1 )-order superconvergence for the error on average on some suitably chosen subdomains (including the whole domain) and their outflow faces. Moreover, we also establish a derivative recovery formula for the approximation of the convection directional derivative which is superconvergent with order k + 1.

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