Abstract
Finite element spaces are constructed that allow for different levels of refinement in different subdomains. In each subdomain the mesh is obtained by several steps of uniform refinement from an initial global coarse mesh. The approximation properties of the resulting discrete space are studied. Computationally feasible, bounded extension operators, from the interface into the subdomains, are constructed and used in the numerical experiments. These operators provide stable splitting of the composite (global) finite element space into local subdomain spaces (vanishing at the interior interfaces) and the “extended” interface finite element space. They also provide natural domain decomposition type preconditioners involving appropriate subdomain and interface preconditioners. Numerical experiments for 3-d elasticity illustrating the properties of the proposed discretization spaces and the algorithm for the solution of the respective linear system are also presented.
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Dobrev, V., Vassilevski, P. (2001). Local Refinement in Non-overlapping Domain Decomposition. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_31
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DOI: https://doi.org/10.1007/3-540-45262-1_31
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