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Time domain computational modelling of 1D arterial networks in monochorionic placentas

Victoria E. Franke, Kim H. Parker, Ling Y. Wee, Nicholas M. Fisk, Spencer J. Sherwin (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we outline the hyperbolic system of governing equations describing one-dimensional blood flow in arterial networks. This system is numerically discretised using a discontinuous Galerkin formulation with a spectral/ h p element spatial approximation. We apply the numerical model to arterial networks in the placenta. Starting with a single placenta we investigate the velocity waveform in the umbilical artery and its relationship with the distal bifurcation geometry and the terminal resistance....

Time domain computational modelling of 1D arterial networks in monochorionic placentas

Victoria E. Franke, Kim H. Parker, Ling Y. Wee, Nicholas M. Fisk, Spencer J. Sherwin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we outline the hyperbolic system of governing equations describing one-dimensional blood flow in arterial networks. This system is numerically discretised using a discontinuous Galerkin formulation with a spectral/hp element spatial approximation. We apply the numerical model to arterial networks in the placenta. Starting with a single placenta we investigate the velocity waveform in the umbilical artery and its relationship with the distal bifurcation geometry and the terminal resistance....

Two-grid finite-element schemes for the transient Navier-Stokes problem

Vivette Girault, Jacques-Louis Lions (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size H . In the second step, the problem is linearized by substituting into the non-linear term, the velocity 𝐮 H computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size h . This approach is motivated by the fact that,...

Two-grid finite-element schemes for the transient Navier-Stokes problem

Vivette Girault, Jacques-Louis Lions (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We semi-discretize in space a time-dependent Navier-Stokes system on a three-dimensional polyhedron by finite-elements schemes defined on two grids. In the first step, the fully non-linear problem is semi-discretized on a coarse grid, with mesh-size H. In the second step, the problem is linearized by substituting into the non-linear term, the velocity uH computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size h. This approach is motivated by the fact that,...

Two-level stabilized nonconforming finite element method for the Stokes equations

Haiyan Su, Pengzhan Huang, Xinlong Feng (2013)

Applications of Mathematics

In this article, we present a new two-level stabilized nonconforming finite elements method for the two dimensional Stokes problem. This method is based on a local Gauss integration technique and the mixed nonconforming finite element of the N C P 1 - P 1 pair (nonconforming linear element for the velocity, conforming linear element for the pressure). The two-level stabilized finite element method involves solving a small stabilized Stokes problem on a coarse mesh with mesh size H and a large stabilized Stokes...

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