Document Zbl 1261.65128

Blanco, Pablo J.; Discacciati, Marco; Quarteroni, Alfio

Modeling dimensionally-heterogeneous problems: Analysis, approximation and applications. (English) Zbl 1261.65128

Numer. Math. 119, No. 2, 299-335 (2011).

Summary: A general theoretical framework for coupled dimensionally-heterogeneous partial differential equations is developed. This is done by recasting the variational formulation in terms of coupling interface variables. In such a general setting we analyze existence and uniqueness of solutions for both the continuous problem and its finite dimensional approximation. This approach also allows the development of different iterative substructuring solution methodologies involving dimensionally-homogeneous subproblems. Numerical experiments are carried out to test our theoretical results.

Reviewer: Zhaoxia Liu (Beijing)

Cited in 10 Documents

MSC:

65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs
35G20	Nonlinear higher-order PDEs
35A15	Variational methods applied to PDEs

Keywords:

variational formulation; iterative substructuring solution methodologies; numerical experiments

Software:

rbMIT

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References:

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