کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4642764 | 1632056 | 2007 | 24 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: An augmented mixed finite element method with Lagrange multipliers: A priori and a posteriori error analyses An augmented mixed finite element method with Lagrange multipliers: A priori and a posteriori error analyses](/preview/png/4642764.png)
In this paper, we provide a priori and a posteriori error analyses of an augmented mixed finite element method with Lagrange multipliers applied to elliptic equations in divergence form with mixed boundary conditions. The augmented scheme is obtained by including the Galerkin least-squares terms arising from the constitutive and equilibrium equations. We use the classical Babuška–Brezzi theory to show that the resulting dual-mixed variational formulation and its Galerkin scheme defined with Raviart–Thomas spaces are well posed, and also to derive the corresponding a priori error estimates and rates of convergence. Then, we develop a reliable and efficient residual-based a posteriori error estimate and a reliable and quasi-efficient Ritz projection-based one, as well. Finally, several numerical results illustrating the performance of the augmented scheme and the associated adaptive algorithms are reported.
Journal: Journal of Computational and Applied Mathematics - Volume 200, Issue 2, 15 March 2007, Pages 653–676