References & Citations
Mathematics > Numerical Analysis
Title: Hybrid Localized Spectral Decomposition for multiscale problems
(Submitted on 27 Jun 2017 (v1), last revised 25 Apr 2024 (this version, v3))
Abstract: We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the unknowns through elliptic problems and satisfies equilibrium constraints. One of the resulting problems is non-local but with exponentially decaying solutions, enabling a practical scheme where the basis functions have an extended, but still local, support. We obtain quasi-optimal a priori error estimates for low-contrast problems assuming minimal regularity of the solutions.
To also consider the high-contrast case, we propose a variant of our method, enriching the space solution via local eigenvalue problems and obtaining optimal a priori error estimate that mitigates the effect of having coefficients with different magnitudes and again assuming no regularity of the solution. The technique developed is dimensional independent and easy to extend to other problems such as elasticity.
Submission history
From: Alexandre Madureira [view email][v1] Tue, 27 Jun 2017 17:01:31 GMT (33kb)
[v2] Mon, 10 Jul 2017 21:16:49 GMT (34kb)
[v3] Thu, 25 Apr 2024 20:47:00 GMT (1025kb,D)
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