Geodesic
On one approach to constructing schemes of increased order of accuracy in the finite element method
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 4, pp. 287-300

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The paper considers schemes of increased order of accuracy in the finite element method with the same number of degrees of freedom as in the schemes constructed by the Galerkin method with the use of piecewisepolynomial functions. The approach proposed is based on a special choice of the grid scalar products and the right-hand side linear functionals limited on a set of grid functions. The fourth order of accuracy is established in the grid energy norm. 
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     author = {A. A. Bubyakin and Yu. M. Laevsky},
     title = {On one approach to constructing schemes of increased order of accuracy in the finite element method},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {287--300},
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     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2004_7_4_a1/}
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A. A. Bubyakin; Yu. M. Laevsky. On one approach to constructing schemes of increased order of accuracy in the finite element method. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 4, pp. 287-300. http://geodesic.mathdoc.fr/item/SJVM_2004_7_4_a1/