On the Convergence of Finite-Element Approximations of a Relaxed Variational Problem
The accuracy of finite-element approximations to a convex, but not strictly convex, variational problem is considered. Convergence is proved for a finite-element approximation of a particular vector field related to the solution. In a special one-dimensional case, 0(h) convergence is shown for a pie...
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| Veröffentlicht in: | SIAM journal on numerical analysis 1990-04, Vol.27 (2), p.419-436 |
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| container_end_page | 436 |
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| container_title | SIAM journal on numerical analysis |
| container_volume | 27 |
| creator | French, Donald A. |
| description | The accuracy of finite-element approximations to a convex, but not strictly convex, variational problem is considered. Convergence is proved for a finite-element approximation of a particular vector field related to the solution. In a special one-dimensional case, 0(h) convergence is shown for a piecewise linear approximation of the derivative. h denotes the size of each element domain. Numerical results are also presented for this one-dimensional case. |
| doi_str_mv | 10.1137/0727025 |
| format | Article |
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| identifier | ISSN: 0036-1429 |
| ispartof | SIAM journal on numerical analysis, 1990-04, Vol.27 (2), p.419-436 |
| issn | 0036-1429 1095-7170 |
| language | eng |
| recordid | cdi_proquest_journals_923293554 |
| source | SIAM Journals Online; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | Approximation Boundary conditions Design optimization Eigenvalues Exact sciences and technology Mathematical constants Mathematics Numerical analysis Numerical analysis. Scientific computation Partial differential equations, boundary value problems Sciences and techniques of general use Simpsons rule Vector fields |
| title | On the Convergence of Finite-Element Approximations of a Relaxed Variational Problem |
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