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On Superconvergence of a Gradient for Finite Element Methods for an Elliptic Equation with the Nonsmooth Right–hand Side
| Content Provider | Scilit |
|---|---|
| Author | Zlotnik, Alexander |
| Copyright Year | 2002 |
| 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. |
| Related Links | http://www.degruyter.com/downloadpdf/j/cmam.2002.2.issue-3/cmam-2002-0018/cmam-2002-0018.xml http://www.degruyter.com/dg/viewarticle.fullcontentlink:pdfeventlink/$002fj$002fcmam.2002.2.issue-3$002fcmam-2002-0018$002fcmam-2002-0018.pdf?t:ac=j$002fcmam.2002.2.issue-3$002fcmam-2002-0018$002fcmam-2002-0018.xml |
| Ending Page | 321 |
| Page Count | 27 |
| Starting Page | 295 |
| ISSN | 16094840 |
| e-ISSN | 16099389 |
| DOI | 10.2478/cmam-2002-0018 |
| Journal | Computational Methods in Applied Mathematics |
| Issue Number | 3 |
| Volume Number | 2 |
| Language | English |
| Publisher | Walter de Gruyter GmbH |
| Publisher Date | 2002-01-01 |
| Access Restriction | Open |
| Subject Keyword | Computational Methods in Applied Mathematics Mathematical Physics Finite Element Methods Superconvergence Nonsmooth Right Elliptic Equation Gradient Hand Side Journal: Computational Methods in Applied Mathematics, Issue- 2 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Numerical Analysis Computational Mathematics |
