Mortar element methods for parabolic problems. (English) Zbl 1156.65083
A standard mortar finite element method and a mortar element method with Lagrange multiplier are used for spatial discretization of a class of parabolic initial-boundary value problems [cf. S. Gaiffe, R. Glowinski, and R. Mason, Numer. Math. 93, No. 1, 53–75 (2002; Zbl 1010.65037) and X.-J. Xu and J. Chen, J. Comput. Math. 21, No. 4, 411–420 (2003; Zbl 1050.65091)].
The authors establish optimal error estimates in \(L^\infty (L^2)\) and \(L^\infty (H^1)\)-norms for semidiscrete methods for both the cases. The key feature adopted here is to introduce a modified elliptic projection. Some numerical examples are given which support the theoretical results.
The authors establish optimal error estimates in \(L^\infty (L^2)\) and \(L^\infty (H^1)\)-norms for semidiscrete methods for both the cases. The key feature adopted here is to introduce a modified elliptic projection. Some numerical examples are given which support the theoretical results.
Reviewer: H. P. Dikshit (Bhopal)
MSC:
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35K15 | Initial value problems for second-order parabolic equations |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
Keywords:
mortar element method; Lagrange multiplier; semidiscretization; backward Euler method; modified elliptic projection; numerical experiments; optimal error estimates; convergence; parabolic initial-boundary value problemsReferences:
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