scholarly journals Finite element approximation of steady flows of generalized Newtonian fluids with concentration-dependent power-law index

2018 ◽  
Vol 88 (317) ◽  
pp. 1061-1090 ◽  
Author(s):  
Seungchan Ko ◽  
Endre Süli
Keyword(s):  
Finite Element ◽  
Power Law ◽  
Finite Element Approximation ◽  
Newtonian Fluids ◽  
Element Approximation ◽  
Steady Flows ◽  
Generalized Newtonian Fluids ◽  
Power Law Index

scholarly journals Finite element approximation of an incompressible chemically reacting non-Newtonian fluid

2018 ◽  
Vol 52 (2) ◽  
pp. 509-541 ◽  
Author(s):  
Seungchan Ko ◽  
Petra Pustějovská ◽  
Endre Süli
Keyword(s):  
Finite Element ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Newtonian Fluid ◽  
Power Law ◽  
Nonlinear Partial Differential Equations ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Partial Differential ◽  
Chemically Reacting

We consider a system of nonlinear partial differential equations modelling the steady motion of an incompressible non-Newtonian fluid, which is chemically reacting. The governing system consists of a steady convection-diffusion equation for the concentration and the generalized steady Navier–Stokes equations, where the viscosity coefficient is a power-law type function of the shear-rate, and the coupling between the equations results from the concentration-dependence of the power-law index. This system of nonlinear partial differential equations arises in mathematical models of the synovial fluid found in the cavities of moving joints. We construct a finite element approximation of the model and perform the mathematical analysis of the numerical method in the case of two space dimensions. Key technical tools include discrete counterparts of the Bogovskiĭ operator, De Giorgi’s regularity theorem in two dimensions, and the Acerbi–Fusco Lipschitz truncation of Sobolev functions, in function spaces with variable integrability exponents.

scholarly journals Finite element analysis of the stationary power-law Stokes equations driven by friction boundary conditions

2015 ◽  
Vol 23 (1) ◽  
Author(s):  
Jules K. Djoko ◽  
Mohamed Mbehou
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Power Law ◽  
Stokes Equations ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Mixed Variational Inequality ◽  
Element Analysis ◽  
Slip Boundary ◽  
Nonlinear Slip Boundary Conditions

AbstractIn this work, we are concerned with the finite element approximation for the stationary power law Stokes equations driven by nonlinear slip boundary conditions of ‘friction type’. After the formulation of the problem as mixed variational inequality of second kind, it is shown by application of a variant of Babuska-Brezzi’s theory for mixed problems that convergence of the finite element approximation is achieved with classical assumptions on the regularity of the weak solution. Next, solution algorithm for the mixed variational problem is presented and analyzed in details. Finally, numerical simulations that validate the theoretical findings are exhibited.

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