.png){kind=icon}
.png){kind=icon}
Return
Parameter robust isogeometric methods for a four-field formulation of Biot's consolidation model
.png){kind=icon}
PRE
AI
H
L
DOI：10.1142/S0218202525500150.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
In this paper, a novel isogeometric method for Biot's consolidation model is constructed and analyzed, using a four-field formulation where the unknown variables are the solid displacement, solid pressure, fluid flux, and fluid pressure. Mixed isogeometric spaces based on B-splines basis functions are employed in the space discretization, allowing a smooth representation of the problem geometry and solution fields. The main result of the paper is the proof of optimal error estimates that are robust with respect to material parameters for all solution fields, particularly in the case of nearly incompressible materials. The analysis does not require a uniformly positive storage coefficient. The results of numerical experiments in two and three dimensions confirm the theoretical error estimates and high-order convergence rates attained by the proposed isogeometric Biot discretization and assess its performance with respect to the mesh size, spline polynomial degree, spline regularity, and material parameters.
Keywords:
Isogeometric analysis
B-splines
Biot's consolidation model
error estimates
mixed isogeometric spaces
inf-sup condition
high-order convergence
Journal
IF:
3
Papers:
2.2K
Citations:
4.6K
Organization
Cited Papers