Coefficient-explicit Condition Number Bounds for Overlapping Additive Schwarz
نویسندگان
چکیده
In this paper we discuss new domain decomposition preconditioners for piecewise linear finite element discretisations of boundary-value problems for the model elliptic problem −∇ · (A∇u) = f , (1) in a bounded polygonal or polyhedral domain Ω ⊂ R, d = 2 or 3 with suitable boundary data on the boundary ∂Ω. The tensor A(x) is assumed isotropic and symmetric positive definite, but may vary with many orders of magnitude in an unstructured way on Ω. Many examples arise in groundwater flow and oil reservoir modelling. Let T h be a conforming shape-regular simplicial mesh on Ω and let S(Ω) denote the space of continuous piecewise linear finite elements on T . The finite element discretisation of (1) in V (the n-dimensional subspace of functions in S(Ω) which vanish on essential boundaries), yields the linear system:
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