The construction of preconditioners for elliptic problems by substructuring. I
Mathematics of Computation
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Adaptive finite element-boundary solution of boundary value problems
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
A Multigrid Algorithm for the Mortar Finite Element Method
SIAM Journal on Numerical Analysis
Domain decomposition methods via boundary integral equations
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Multiplier Spaces for the Mortar Finite Element Method in Three Dimensions
SIAM Journal on Numerical Analysis
On the stability of the L2 projection in H1(Ω)
Mathematics of Computation
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In this paper a natural domain decomposition method based on local Dirichlet-Neumann maps is considered. The global variational problem is defined on the skeleton of the domain decomposition only. For the approximation of the Dirichlet-Neumann maps Dirichlet boundary value problems need to be solved locally. The local finite element spaces within the subdomains can be chosen independently of the global trial space on the skeleton. In particular, this approach can be used to couple non-matching triangulations across the interfaces without an additional framework such as introducing Lagrange multipliers. Numerical results for two model problems confirm the stability and error estimates given here.