The version of Eulerian-Lagrangian mixed discontinuous finite element methods for advection-diffusion problems.
The heat transform and its use in thermal identification problems for electronic circuits.
The invertibility of the isoparametric mappings for triangular quadratic Lagrange finite elements
A reference triangular quadratic Lagrange finite element consists of a right triangle with unit legs , , a local space of quadratic polynomials on and of parameters relating the values in the vertices and midpoints of sides of to every function from . Any isoparametric triangular quadratic Lagrange finite element is determined by an invertible isoparametric mapping . We explicitly describe such invertible isoparametric mappings for which the images , of the segments , are segments,...
The local projection -discontinuous-Galerkin finite element method for scalar conservation laws
The version of mixed finite element methods for parabolic problems
The Runge-Kutta local projection -discontinuous-Galerkin finite element method for scalar conservation laws
The sinc-Galerkin method for solving singularly-perturbed reaction-diffusion problem.
The stability of Ritz-Volterra projection and error estimates for finite element methods for a class of integro-differential equations of parabolic type
In this paper we first study the stability of Ritz-Volterra projection (see below) and its maximum norm estimates, and then we use these results to derive some error estimates for finite element methods for parabolic integro-differential equations.
Theoretical and numerical studies of the DG schemes in one space dimension
We give a proof of the existence of a solution of reconstruction operators used in the DG schemes in one space dimension. Some properties and error estimates of the projection and reconstruction operators are presented. Then, by applying the DG schemes to the linear advection equation, we study their stability obtaining maximal limits of the Courant numbers for several DG schemes mostly experimentally. A numerical study explains how the stencils used in the reconstruction affect the efficiency...
Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion
We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine a-priori estimates are derived, and convergence is proved by careful successive...
Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion*
We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine a-priori estimates are derived, and convergence is proved by careful...
Time discretization of parabolic problems by the discontinuous Galerkin method
Time domain computational modelling of 1D arterial networks in monochorionic placentas
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/ 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
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....
Time-discrete finite element schemes for Maxwell's equations
Tuning the mesh of a mixed method for the stream function. Vorticity formulation of the Navier-Stokes equations.
Two-grid finite-element schemes for the transient Navier-Stokes problem
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 . In the second step, the problem is linearized by substituting into the non-linear term, the velocity computed at step one, and the linearized problem is semi-discretized on a fine grid with mesh-size . This approach is motivated by the fact that,...
Two-grid finite-element schemes for the transient Navier-Stokes problem
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
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 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 and a large stabilized Stokes...
Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik.