We propose and analyze a domain decomposition method on non-matching grids for partial differential equations with non-negative characteristic form. No weak or strong continuity of the finite element functions, their normal derivatives, or linear combinations of the two is imposed across the boundaries of the subdomains. Instead, we employ suitable bilinear forms defined on the common interfaces, typical of discontinuous Galerkin approximations. We prove an error bound which is optimal with respect...
We propose and analyze a domain decomposition method on non-matching grids
for partial differential equations with non-negative
characteristic form. No weak or strong continuity of the finite
element functions, their normal derivatives, or linear
combinations of the two is imposed across the boundaries of the subdomains.
Instead, we employ suitable bilinear forms defined on the common
interfaces, typical of discontinuous Galerkin
approximations.
We prove an error bound which is optimal with respect...
In this paper, we present extensive numerical tests showing the performance
and robustness of a Balancing Neumann-Neumann method for the solution of algebraic linear systems arising from finite element approximations of scalar elliptic
problems on geometrically refined boundary layer meshes in
three dimensions. The numerical results are in good agreement with the theoretical bound for the condition number of the preconditioned operator derived in [Toselli and Vasseur,
(2004) 123–156]....
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