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Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 09/2017, Volume 324, pp. 29 - 53
The multiscale hybrid-mixed (MHM) method is extended to the Stokes and Brinkman equations with highly heterogeneous coefficients. The approach is constructive.... 
Brinkman model | Hybrid method | Multiscale finite element | Stokes equation | Mixed method | DARCY FLOW | FINITE-ELEMENT METHODS | BUBBLES | ELLIPTIC PROBLEMS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | DISCONTINUOUS GALERKIN METHODS | COEFFICIENTS | ENRICHMENT | POROUS-MEDIA
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 8/2019, Volume 58, Issue 4, pp. 1 - 31
In this paper, we study a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn–Hilliard type... 
35K61 | 49K20 | 49J20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 76D07 | 92C50 | MATHEMATICS | MATHEMATICS, APPLIED | DARCY SYSTEM | CHEMOTAXIS | GROWTH | WELL-POSEDNESS | TIME | SIMULATION | DIFFUSE INTERFACE MODEL | Drugs | Drug therapy | Tumors
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 10/2018, Volume 69, Issue 5, pp. 1 - 18
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 04/2013, Volume 23, Issue 4, pp. 671 - 741
We develop divergence-conforming B-spline discretizations for the numerical solution of the Darcy-Stokes-Brinkman equations. These discretizations are... 
generalized Stokes equations | Darcy-Stokes-Brinkman equations | divergence-conforming discretizations | B-splines | isogeometric analysis | SYSTEM | MATHEMATICS, APPLIED | P-VERSION | H(DIV) | HYBRIDIZATION | FLOW | DIRICHLET BOUNDARY-CONDITIONS | MASS CONSERVATION | DISCRETE | COMPUTATIONAL FLUID-DYNAMICS | FINITE-ELEMENT-METHOD
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 04/2019, Volume 266, Issue 9, pp. 5998 - 6036
Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn–Hilliard... 
Brinkman's law | Chemotaxis | Cahn–Hilliard equation | Outflow conditions | Tumour growth | Stokes flow | MATHEMATICS | Cahn-Hilliard equation | INVASION | DARCY SYSTEM | WELL-POSEDNESS | VISCOSITY | NONLINEAR SIMULATION | Analysis | Tumors
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 01/2018, Volume 28, Issue 1, pp. 159 - 194
Journal Article
Journal of Petroleum Science and Engineering, ISSN 0920-4105, 10/2015, Volume 134, pp. 76 - 78
The Darcy–Brinkman equation was evaluated in conditions near to those found in oil extraction problems. The results showed that Darcy formulation is preferable... 
Darcy equation | Brinkman correction | Oil extraction | HEAT | INCOMPRESSIBLE FLUIDS | MODELS | ENERGY & FUELS | CONVECTION | POROUS-MEDIA | EFFECTIVE VISCOSITY | ENGINEERING, PETROLEUM | Petroleum mining | Analysis
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2019, Volume 472, Issue 1, pp. 148 - 175
This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy–Brinkman equations in double-diffusive... 
Darcy–Brinkman | Curvature stabilization | Double diffusion | MATHEMATICS | MATHEMATICS, APPLIED | CAVITY | FINITE-ELEMENT | 2-LEVEL METHOD | Darcy-Brinkman | DIFFUSIVE NATURAL-CONVECTION | OPPOSING TEMPERATURE | SCHEMES
Journal Article
Monatshefte fur Mathematik, ISSN 0026-9255, 06/2017, Volume 183, Issue 2, pp. 269 - 302
The purpose of this paper is to develop a layer potential analysis in order to show the well-posedness result of a transmission problem for the Oseen and... 
Oseen system | Transmission problem | solution | Brinkman system | Layer potential operators | Existence and uniqueness results | LAPLACE EQUATION | STOKES SYSTEM | L-q-solution | BOUNDARY-VALUE-PROBLEMS | LIPSCHITZ-DOMAINS | JUMP PROBLEM | TRANSMISSION PROBLEMS | MATHEMATICS | DIRICHLET PROBLEM | ELLIPTIC-SYSTEMS | DARCY-FORCHHEIMER-BRINKMAN | INTEGRAL-OPERATORS
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 08/2016, Volume 39, Issue 12, pp. 3328 - 3349
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 2007, Volume 385, Issue 1, pp. 69 - 79
Up-scaling of the Stokes equations with non-slip boundary condition describing the flow in a porous medium, leads to the Darcy–Brinkman equation ɛ β μ β v D ,... 
Porous media | Volume averaging | Darcy–Brinkman equation | Slip boundary conditions | Darcy-Brinkman equation | TRANSPORT | MOTION | LAW | PHYSICS, MULTIDISCIPLINARY | volume averaging | POROUS-MEDIA | porous media | slip boundary conditions | FLOW | Computer simulation | Computer-generated environments | Porosity
Journal Article
Transport in Porous Media, ISSN 0169-3913, 3/2017, Volume 117, Issue 1, pp. 27 - 44
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 10/2014, Volume 244, pp. 201 - 208
In this paper, we consider the nonhomogeneous Brinkman–Forchheimer equations in a semi-infinite pipe. Continuous dependence for the Brinkman–Forchheimer... 
Saint-Venant principle | Continuous dependence | Brinkman–Forchheimer equations | Brinkman-Forchheimer equations | STRUCTURAL STABILITY | MATHEMATICS, APPLIED | INEQUALITIES | MODEL | FLOW | POROUS PENETRATIVE CONVECTION | CONVERGENCE | MEDIA | DARCY EQUATIONS | GEOMETRY
Journal Article
Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 03/2019, Volume 35, Issue 2, pp. 509 - 527
In this paper, we consider the mark and cell (MAC) method for Darcy‐Stokes‐Brinkman equations and analyze the stability and convergence of the method on... 
the MAC scheme | Darcy‐Stokes‐Brinkman equations | error analysis | stability | non‐uniform grids | Darcy-Stokes-Brinkman equations | non-uniform grids | MATHEMATICS, APPLIED | SUPERCONVERGENCE | APPROXIMATIONS | MAC SCHEME | ELEMENT METHODS | Stability analysis | Parameters | Velocity | Convergence | Finite difference method
Journal Article
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, ISSN 0036-1410, 2019, Volume 51, Issue 3, pp. 1868 - 1912
In this work, we study a model consisting of a Cahn-Hilliard-type equation for the concentration of tumor cells coupled to a reaction-diffusion-type equation... 
Cahn-Hilliard equation | MATHEMATICS, APPLIED | WELL-POSEDNESS | outflow conditions | FLOW | Darcy flow | DARCY SYSTEM | tumor growth | HELE-SHAW SYSTEM | Brinkman's law | EQUATION | NONLINEAR SIMULATION | chemotaxis | Stokes flow
Journal Article
Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 11/2017, Volume 33, Issue 6, pp. 1949 - 1965
In this work, we propose and analyze the pressure stabilization method for the unsteady incompressible Brinkman‐Forchheimer equations. We present a time... 
stability | continuous dependence | brinkman equations | EXISTENCE | MATHEMATICS, APPLIED | PSEUDOCOMPRESSIBILITY METHOD | PROJECTION METHODS | FLOW | ATTRACTORS | NAVIER-STOKES EQUATIONS | CONVERGENCE | POROUS-MEDIA | DARCY EQUATIONS | Finite element method | Approximation | Computational fluid dynamics | Mathematical analysis | Stabilization | Numerical Analysis | Mathematics
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 08/2016, Volume 307, pp. 68 - 95
Journal Article
Transport in Porous Media, ISSN 0169-3913, 2009, Volume 79, Issue 2, pp. 215 - 223
An increasing number of articles are adopting Brinkman's equation in place of Darcy's law for describing flow in porous media. That poses the question of the... 
Effective viscosity | Darcy's law | Domain of validity | Brinkman's equation | NUMBER | RANDOM ARRAY | FLUID-FLOW | PARTICLES | SPHERES | MODEL | ENGINEERING, CHEMICAL | SUSPENSION | STOKES PROBLEM | SCALES | POROUS-MEDIA | Permeability | Fluid dynamics | Low concentrations | Newtonian fluids | Mathematical analysis | Fluid flow | Media | Porosity | Three dimensional
Journal Article
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