The Stabilized Three-Field Domain Decomposition Method
DOI:
https://doi.org/10.5540/03.2026.012.01.0339Palavras-chave:
Hybrid Method, Stabilized Method, Hybrid Mixed Method, Finite Element Method, Multiscale-Hybrid-Hybrid Mixed Method, Numerical NethodResumo
In this work we consider the Three-Field finite element formulation for elliptic problems. In the original setting, not all combinations of spaces will lead to stable formulations, and two independent inf-sup conditions must be satisfied. One way to relax such constraint is to introduce stabilizations terms, allowing more space choices. Our goal is to propose a stabilized scheme that allows different combinations of polynomials for the unknowns involved. We explore here the possibility of employing the three-field formulation as a direct method, i.e., no submeshes involved. We show coercivity and convergence results in a suitable mesh dependent norm. Efficient implementation of the method is still possible, as static condensation of the unknowns can be performed at the element level, in parallel. We present numerical results displaying the performance of the method.
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Referências
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