Two-Grid Methods for Mixed Finite Element Approximations of Nonlinear Parabolic Equations
| dc.contributor.author | Dawson, Clint N. | en_US |
| dc.contributor.author | Wheeler, Mary F. | en_US |
| dc.date.accessioned | 2018-06-18T17:41:49Z | en_US |
| dc.date.available | 2018-06-18T17:41:49Z | en_US |
| dc.date.issued | 1994-01 | en_US |
| dc.date.note | January 1994 | en_US |
| dc.description.abstract | Mixed finite element approximation of nonlinear parabolic equations is discussed. The equation considered is a prototype of a model which arises in flow through porous media. A two-grid approximation scheme is developed and analyzed for implicit time discretizations. In this approach, the full nonlinear system is solved on a "coarse" grid of size H. The nonlinearities are expanded about the coarse grid solution, and the resulting linear but nonsymmetric system is solved on a "fine" grid of size h. Error estimates are derived which demonstrate that the error is O (h^{k+1} + H^{2(k+1)-d/2} + Deltat), where k is the degree of the approximating space for the primary variable and d is spatial dimension, with k >= 1 for d >= 2. For the RT0 space (k=0) on rectangular domains, we present a modified scheme for treating the coarse grid problem. Here we show that the error is O (h + H^{3 - d/2} + Deltat). The above estimates are useful for determining an appropriate H for the coarse grid problem. | en_US |
| dc.format.extent | 13 pp | en_US |
| dc.identifier.citation | Dawson, Clint N. and Wheeler, Mary F.. "Two-Grid Methods for Mixed Finite Element Approximations of Nonlinear Parabolic Equations." (1994) <a href="https://hdl.handle.net/1911/101826">https://hdl.handle.net/1911/101826</a>. | en_US |
| dc.identifier.digital | TR94-01 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/101826 | en_US |
| dc.language.iso | eng | en_US |
| dc.title | Two-Grid Methods for Mixed Finite Element Approximations of Nonlinear Parabolic Equations | en_US |
| dc.type | Technical report | en_US |
| dc.type.dcmi | Text | en_US |
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