Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
Mixed discontinuous Galerkin approximation of the Maxwell operator : the indefinite case
We present and analyze an interior penalty method for the numerical discretization of the indefinite time-harmonic Maxwell equations in mixed form. The method is based on the mixed discretization of the curl-curl operator developed in [Houston et al., J. Sci. Comp. 22 (2005) 325–356] and can be understood as a non-stabilized variant of the approach proposed in [Perugia et al., Comput. Methods Appl. Mech. Engrg. 191 (2002) 4675–4697]. We show the well-posedness of this approach and derive optimal...
Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case
We present and analyze an interior penalty method for the numerical discretization of the indefinite time-harmonic Maxwell equations in mixed form. The method is based on the mixed discretization of the curl-curl operator developed in [Houston et al., J. Sci. Comp.22 (2005) 325–356] and can be understood as a non-stabilized variant of the approach proposed in [Perugia et al., Comput. Methods Appl. Mech. Engrg.191 (2002) 4675–4697]. We show the well-posedness of this approach and derive optimal...
Mixed finite element approximation for a coupled petroleum reservoir model
In this paper, we are interested in the modelling and the finite element approximation of a petroleum reservoir, in axisymmetric form. The flow in the porous medium is governed by the Darcy-Forchheimer equation coupled with a rather exhaustive energy equation. The semi-discretized problem is put under a mixed variational formulation, whose approximation is achieved by means of conservative Raviart-Thomas elements for the fluxes and of piecewise constant elements for the pressure and the temperature....
Mixed finite element approximation for a coupled petroleum reservoir model
In this paper, we are interested in the modelling and the finite element approximation of a petroleum reservoir, in axisymmetric form. The flow in the porous medium is governed by the Darcy-Forchheimer equation coupled with a rather exhaustive energy equation. The semi-discretized problem is put under a mixed variational formulation, whose approximation is achieved by means of conservative Raviart-Thomas elements for the fluxes and of piecewise constant elements for the pressure and the temperature....
Mixed finite element methods for quasilinear second order elliptic problems : the -version
Mixed Finite Elements for Second Order Elliptic Problems in Three Variables.
Mixed-hybrid model of the fracture flow
Mortar spectral element discretization of the Laplace and Darcy equations with discontinuous coefficients
This paper deals with the mortar spectral element discretization of two equivalent problems, the Laplace equation and the Darcy system, in a domain which corresponds to a nonhomogeneous anisotropic medium. The numerical analysis of the discretization leads to optimal error estimates and the numerical experiments that we present enable us to verify its efficiency.
Mortar spectral method in axisymmetric domains
We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy of our discretization.
Mortar spectral method in axisymmetric domains
We consider the Laplace equation posed in a three-dimensional axisymmetric domain. We reduce the original problem by a Fourier expansion in the angular variable to a countable family of two-dimensional problems. We decompose the meridian domain, assumed polygonal, in a finite number of rectangles and we discretize by a spectral method. Then we describe the main features of the mortar method and use the algorithm Strang Fix to improve the accuracy...
Multigrid for the Wilson mortar element method.
Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem
Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem
In this paper, a multi-parameter error resolution technique is applied into a mixed finite element method for the Stokes problem. By using this technique and establishing a multi-parameter asymptotic error expansion for the mixed finite element method, an approximation of higher accuracy is obtained by multi-processor computers in parallel.
-widths for singularly perturbed problems
-widths for singularly perturbed problems
Kolmogorov -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.
New Error Bounds for the Penalty Method and Extrapolation.
New mixed finite volume methods for second order eliptic problems
In this paper we introduce and analyze new mixed finite volume methods for second order elliptic problems which are based on H(div)-conforming approximations for the vector variable and discontinuous approximations for the scalar variable. The discretization is fulfilled by combining the ideas of the traditional finite volume box method and the local discontinuous Galerkin method. We propose two different types of methods, called Methods I and II, and show that they have distinct advantages over...
New quadrilateral mixed finite elements.
New regularity results and improved error estimates for optimal control problems with state constraints
In this paper we are concerned with a distributed optimal control problem governed by an elliptic partial differential equation. State constraints of box type are considered. We show that the Lagrange multiplier associated with the state constraints, which is known to be a measure, is indeed more regular under quite general assumptions. We discretize the problem by continuous piecewise linear finite elements and we are able to prove that, for the case of a linear equation, the order of convergence...