Pani, Amiya K. ; Fairweather, Graeme (2003) An H1-Galerkin mixed finite element method for an evolution equation with a positive-type memory term SIAM Journal on Numerical Analysis, 40 (4). pp. 1475-1490. ISSN 0036-1429
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Official URL: http://epubs.siam.org/sinum/resource/1/sjnaam/v40/...
Related URL: http://dx.doi.org/10.1137/S0036142900372318
Abstract
An H1-Galerkin mixed finite element method is analyzed for a class of evolution equations with memory. When a classical mixed method is applied to such problems, it has not been possible to obtain any estimate for the flux. However, the proposed approach yields optimal order convergence without the LBB consistency condition and quasi uniformity of the finite element mesh. Compared to the results proved for one space variable, the L2 estimate of the flux is not optimal for problems in two and three space dimensions. Therefore, a modification of the method is proposed and analyzed. A maximum norm estimate is also derived in one and two space variables. A backward Euler approximation of the modified method is also analyzed.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Society for Industrial and Applied Mathematics. |
| Keywords: | Evolution Equation; Several Space Variables; Positive-type Memory; Mixed Finite Element Method; H1-Galerkin; LBB Condition; Semidiscrete Schemes; Backward Euler Method; Optimal Error Estimates; Flux Estimates |
| ID Code: | 81965 |
| Deposited On: | 09 Feb 2012 04:44 |
| Last Modified: | 09 Feb 2012 04:44 |
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