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- W3089963516 abstract "Abstract Solutions of boundary value problems in three‐dimensional domains with edges may exhibit singularities which are known to influence both the accuracy of the finite element solutions and the rate of convergence in the error estimates. This paper considers boundary value problems for the Poisson equation on typical domains Ω ⊂ ℝ 3 with edge singularities and presents, on the one hand, explicit computational formulas for the flux intensity functions. On the other hand, it proposes and analyzes a nonconforming finite element method on regular meshes for the efficient treatment of the singularities. The novelty of the present method is the use of the explicit formulas for the flux intensity functions in defining a postprocessing procedure in the finite element approximation of the solution. A priori error estimates in H 1 (Ω) show that the present algorithm exhibits the same rate of convergence as it is known for problems with regular solutions." @default.
- W3089963516 created "2020-10-08" @default.
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- W3089963516 date "2020-09-28" @default.
- W3089963516 modified "2023-09-26" @default.
- W3089963516 title "Singular solutions of the Poisson equation at edges of three‐dimensional domains and their treatment with a predictor–corrector finite element method" @default.
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- W3089963516 doi "https://doi.org/10.1002/num.22555" @default.
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