Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part II: Mixed-hybrid finite element solution
نویسندگان
چکیده
منابع مشابه
Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part II: Mixed-hybrid finite element solution
The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory. This theory results in a coupled system of nonlinear parabolic differential equations together with an algebraic constraint for electroneutrality. In this model, it is desirable to obtain accurate approximations of the fluid flow and ions flow. Such accurate approximations can be determined by the ...
متن کاملCASA Report, Thechnische Universiteit Eindhoven MATHEMATICAL MODELLING AND NUMERICAL SOLUTION OF SWELLING OF CARTILAGINOUS TISSUES. PART II: MIXED-HYBRID FINITE ELEMENT SOLUTION
The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory. This theory results in a coupled system of nonlinear parabolic differential equations together with an algebraic constraint for electroneutrality. In this model, it is desirable to obtain accurate approximations of the fluid flow and ions flow. Such accurate approximations can be determined by the ...
متن کاملMixed finite element modelling of cartilaginous tissues
Swelling and shrinking of cartilaginous tissues is modelled by a four-component mixture theory. This theory results in a set of coupled non-linear partial differential equations for the electro-chemical potentials and the displacement. For the sake of local mass conservation these equations are discretised in space by a mixed finite element method. Integration in time by backward Euler leads to...
متن کاملCASA Report, Thechnische Universiteit Eindhoven MATHEMATICAL MODELLING AND NUMERICAL SOLUTION OF SWELLING OF CARTILAGINOUS TISSUES. PART I: MODELING OF INCOMPRESSIBLE CHARGED POROUS MEDIA
The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory in which a deformable and charged porous medium is saturated with a fluid with dissolved ions. Four components are defined: solid, liquid, cations and anions. The aim of this paper is the construction of the Lagrangian model of the four-component system. It is shown that, with the choice of Lagrangi...
متن کاملexistence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types
بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی بیان شده اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...
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ژورنال
عنوان ژورنال: ESAIM: Mathematical Modelling and Numerical Analysis
سال: 2007
ISSN: 0764-583X,1290-3841
DOI: 10.1051/m2an:2007037