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- W2123972052 abstract "In early 1970's. we developed idea of conjugate finite element ap- proximations as a means to calculate consistent approximations of various functions. particularly stress fields, in problems of solid mechanics or fluxes. in general (1-4). The original idea was a simple one. based on rather primi- tive notion that operations on functions defined on finite-dimensional. finite- element spaces make most sense when restricted to those spaces. When an operation (such as differentiation) on a function II produces a function ' that does not belong to given finite-dimensional space Sh' then consistent'· approximation of v is simply its projection Ill· back into Sh' Remarkably. a simple L 2-projection of stresses computed using conventional finite element methods produces stress fields that are generally far more accurate than those computed directly from calculated displacements (4) or II (pages 83- 34)). For this reason. L 2-projection of stresses is now in use in many finite ele- ment analyses as a practical device for obtaining improved stress fields. We should mention that there exist several methods for obtaining approxima- tions of gradients of accuracy 0 (112) other than projection ideas covered here; e.g .. one can use superconvergence results and fit splines through stress points at which gradients are superaccurate (5-7) or one can simply use finite difference quotients based on computed displacements IIh (8/. However. our nu- merical experiments (discussed in Section V) indicate that projection tech- niques yield results superior to both superconvergence and difference methods. More importantly. projection methods seem to work for nonuni- form and even unstructured meshes. while other methods. at least in theory. rely heavily on such properties. We should mention also that proposed procedure has features theoreti- cally similar to the method of averaging by Bramble and Schatz (9). How- ever. practical implementations of two approaches are quite different: projection is performed by solving a system of equations (possibly iteratively to" @default.
- W2123972052 created "2016-06-24" @default.
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- W2123972052 date "1989-01-01" @default.
- W2123972052 modified "2023-09-27" @default.
- W2123972052 title "On the accuracy and convergence of conjugate flux approximations" @default.
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- W2123972052 doi "https://doi.org/10.1002/num.1690050208" @default.
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