Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
Mixed approximation of eigenvalue problems: A superconvergence result
We state a superconvergence result for the lowest order Raviart-Thomas approximation of eigenvalue problems. It is known that a similar superconvergence result holds for the mixed approximation of Laplace problem; here we introduce a new proof, since the one given for the source problem cannot be generalized in a straightforward way to the eigenvalue problem. Numerical experiments confirm the superconvergence property and suggest that it also holds for the lowest order Brezzi-Douglas-Marini...
Mixed boundary value problems for nonlinear elliptic systems in -dimensional Lipschitzian domains.
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 approximation of an MHD problem involving conducting and insulating regions : the 2D case
We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge elements.
Mixed Finite Element approximation of an MHD problem involving conducting and insulating regions: the 2D case
We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge elements.
Mixed finite element in 3D in and
Mixed finite element methods for quasilinear second order elliptic problems : the -version
Mixed Finite Elements for Second Order Elliptic Problems in Three Variables.
Mixed formulation of elliptic variational inequalities and its approximation
The approximation of a mixed formulation of elliptic variational inequalities is studied. Mixed formulation is defined as the problem of finding a saddle-point of a properly chosen Lagrangian on a certain convex set . Sufficient conditions, guaranteeing the convergence of approximate solutions are studied. Abstract results are applied to concrete examples.
Mixed interface problems for anisotropic elastic bodies.
Mixed problem for semilinear hyperbolic equation of second order with the Dirichlet boundary condition (Preliminary communication)
Mixed problem for semilinear hyperbolic equation of second order with Dirichlet boundary condition
Mixed problem for the Bellman equation with measurable coefficients.
Mixed problem with boundary integral conditions for a certain parabolic equation.
Mixed problem with boundary integral conditions for a class of hyperbolic equations. (Problème mixte avec conditions intégrales pour une classe d'équations hyperboliques.)
Mixed problem with integral boundary condition for a high order mixed type partial differential equation.