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An additive Schwarz preconditioner for the mortar-type rotated \(Q_1\) FEM for elliptic problems with discontinuous coefficients. (English) Zbl 1162.65408

Summary: We propose an additive Schwarz preconditioner for the mortar-type rotated \(Q_1\) finite element method for second order elliptic partial differential equations with piecewise but discontinuous coefficients. The work here is an extension of the research presented by L. Marcinkowski [BIT 45, 375–394 (2005; Zbl 1080.65118)]. Our analysis is valid for rectangular or L-shaped domains, which are partitioned by rectangular subdomains and meshes. We have shown that our proposed method has a quasi-optimal convergence behavior, i.e., the condition number of the preconditioned problem is O\(((1+\log(H/h))^2)\), which is independent of the jump in the coefficient. Numerical experiments presented in this paper have confirmed our theoretical analysis.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Citations:

Zbl 1080.65118

Software:

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References:

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