Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  study a one-continuum model approach, so-called Brinkman model, to deal with Navier---Stokes---Darcy coupling problem in which the fluid flow exist in both the open channels and porous media. A parameter re-scaling technique is used to reformulate the traditional Brinkman model to a new one in order to investigate its asymptotic accuracy to Stokes and Darcy's equations, respectively.  attain the convergence theorem in quantitative measure with respect to the dimensionless permeability parameter.  also analyze the error estimates of mixed finite element method for Brinkman model and Forchheimer model, and obtain the optimal convergence rates for both velocity and pressure. Numerical experiments validate the convergence results with respect to the permeability parameter and mesh size for both Brinkman model and Forchheimer model.
['Pengtao Sun', 'Yuzhou Sun']
I am writing a research paper on a idea Asymptotic Analysis and Error Estimates of Mixed Finite Element Method for Brinkman Model
[{"from": "human", "value": "I am writing a research paper on a idea Asymptotic Analysis and Error Estimates of Mixed Finite Element Method for Brinkman Model"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  study a one-continuum model approach, so-called Brinkman model, to deal with Navier---Stokes---Darcy coupling problem in which the fluid flow exist in both the open channels and porous media. A parameter re-scaling technique is used to reformulate the traditional Brinkman model to a new one in order to investigate its asymptotic accuracy to Stokes and Darcy's equations, respectively.  attain the convergence theorem in quantitative measure with respect to the dimensionless permeability parameter.  also analyze the error estimates of mixed finite element method for Brinkman model and Forchheimer model, and obtain the optimal convergence rates for both velocity and pressure. Numerical experiments validate the convergence results with respect to the permeability parameter and mesh size for both Brinkman model and Forchheimer model."}]