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- W1996283036 abstract "Abstract The elliptic equation under the nonhomogeneous Dirichlet boundary condition in 2D and 3D cases is solved. A rectangular nonuniform partition of a domain and polylinear finite elements are taken. For the interpolant of the exact solution u , a priori error estimates are proved provided that u possesses a weakened smoothness. Next error estimates are in terms of data. An estimate is established for the right–hand side f of the equation having a generalized smoothness. Error estimates are derived in the case of f which is not compatible with the boundary function. The proofs are based on some propositions from the theory of functions. The corresponding lower error estimates are also included; they justify the sharpness of the estimates without the logarithmic multipliers. Finally, we prove similar results in the case of 2D linear finite elements and a uniform partition." @default.
- W1996283036 created "2016-06-24" @default.
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- W1996283036 date "2002-01-01" @default.
- W1996283036 modified "2023-09-25" @default.
- W1996283036 title "On Superconvergence of a Gradient for Finite Element Methods for an Elliptic Equation with the Nonsmooth Right–hand Side" @default.
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- W1996283036 doi "https://doi.org/10.2478/cmam-2002-0018" @default.
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