Stabilization arising from PGEM: A review and further developments
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Cited by (14)
Revisiting the robustness of the multiscale hybrid-mixed method: The face-based strategy
2024, Journal of Computational and Applied MathematicsFully discrete finite element method based on pressure stabilization for the transient Stokes equations
2012, Mathematics and Computers in SimulationCitation Excerpt :Moreover, The P1–P1 pair is of practical importance in scientific computation with the lowest computational cost. Therefore, much attention has been attracted by the P1–P1 pair for simulating the incompressible flow, we can refer to [1,3,16,20] and the references therein. In order to use the P1–P1 pair, various stabilized techniques have been proposed and studied.
Numerical multiscale methods for a reaction-dominated model
2012, Computer Methods in Applied Mechanics and EngineeringCitation Excerpt :Furthermore, edge residuals play an important role in the construction of enriching basis functions for the reaction–diffusion model [15]. This is, actually, the PGEM’s distinguishing feature (see [18] for an overview) and allows the method to produce solutions which are accurate in natural norms. Other approaches rely on nonstandard polynomial basis functions, such as the PUM (Partition of Unity Method).
Equal-order finite elements with local projection stabilization for the Darcy-Brinkman equations
2011, Computer Methods in Applied Mechanics and EngineeringA residual local projection method for the Oseen equation
2010, Computer Methods in Applied Mechanics and EngineeringA Petrov–Galerkin multiscale hybrid-mixed method for the Darcy equation on polytopes
2023, Computational and Applied Mathematics
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This author is partially supported by FONDECYT Project No. 1070698.
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This author is partially supported by CONICYT-Chile through FONDECYT Project No. 1061032 and FONDAP Program on Applied Mathematics.
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Present address: Department of Mathematics, University of Strathclyde, 26 Richmond street, Glasgow G1 1XH, UK
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This author is partially supported by NSF Grant No. 0610039.
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This author is supported by CNPq grant No. 304051/2006-3 and FAPERJ.