Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
On the interface boundary condition of Beavers, Joseph, and Saffman
SIAM Journal on Applied Mathematics
Navier--Stokes Equations in Rotation Form: A Robust Multigrid Solver for the Velocity Problem
SIAM Journal on Scientific Computing
A Robust Finite Element Method for Darcy--Stokes Flow
SIAM Journal on Numerical Analysis
Coupling Fluid Flow with Porous Media Flow
SIAM Journal on Numerical Analysis
Accuracy and stability of splitting with stabilizing corrections
Applied Numerical Mathematics
Mathematical and numerical models for coupling surface and groundwater flows
Applied Numerical Mathematics
Computing and Visualization in Science
A unified stabilized method for Stokes' and Darcy's equations
Journal of Computational and Applied Mathematics
A Two-Grid Method of a Mixed Stokes-Darcy Model for Coupling Fluid Flow with Porous Media Flow
SIAM Journal on Numerical Analysis
Coupling Stokes and Darcy equations
Applied Numerical Mathematics
Introduction to the Numerical Analysis of Incompressible Viscous Flows
Introduction to the Numerical Analysis of Incompressible Viscous Flows
Preconditioning techniques for a mixed Stokes/Darcy model in porous media applications
Journal of Computational and Applied Mathematics
Coupled Generalized Nonlinear Stokes Flow with Flow through a Porous Medium
SIAM Journal on Numerical Analysis
Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems
SIAM Journal on Numerical Analysis
Finite Element Approximations for Stokes-Darcy Flow with Beavers-Joseph Interface Conditions
SIAM Journal on Numerical Analysis
Stability of two IMEX methods, CNLF and BDF2-AB2, for uncoupling systems of evolution equations
Applied Numerical Mathematics
Hi-index | 7.29 |
This report analyzes the long time stability of four methods for non-iterative, sub-physics, uncoupling for the evolutionary Stokes-Darcy problem. The four methods uncouple each timestep into separate Stokes and Darcy solves using ideas from splitting methods. Three methods uncouple sequentially while one is a parallel uncoupling method. We prove long time stability of four splitting based partitioned methods under timestep restrictions depending on the problem parameters. The methods include those that are stable uniformly in S"0, the storativity coefficient, for moderate k"m"i"n, the minimum hydraulic conductivity, uniformly in k"m"i"n for moderate S"0 and with no coupling between the timestep and the spacial meshwidth.