Finite element approximation of nonlinear elliptic problems with discontinuous coefficients
Finite element convergence for the Darwin model to Maxwell's equations
Finite Element Error Estimates for Non-Linear Elliptic Equations of Monotone Type.
Finite Element Methods for Nonlinear Shell Analysis.
Finite element methods for solving the stationary Stokes and Navier-Stokes equations
Finite element solution of a nonlinear diffusion problem with a moving boundary
Finite element solution of a nonlinear diffusion problem with a moving boundary
Finite volume box schemes and mixed methods
Finite Volume Box Schemes and Mixed Methods
We present the numerical analysis on the Poisson problem of two mixed Petrov-Galerkin finite volume schemes for equations in divergence form . The first scheme, which has been introduced in [CITE], is a generalization in two dimensions of Keller's box-scheme. The second scheme is the dual of the first one, and is a cell-centered scheme for u and the flux φ. For the first scheme, the two trial finite element spaces are the nonconforming space of Crouzeix-Raviart for the primal unknown u...
Finite volume box schemes on triangular meshes
Finite volume methods for elliptic PDE’s : a new approach
We consider a new formulation for finite volume element methods, which is satisfied by known finite volume methods and it can be used to introduce new ones. This framework results by approximating the test function in the formulation of finite element method. We analyze piecewise linear conforming or nonconforming approximations on nonuniform triangulations and prove optimal order norm and norm error estimates.
Finite Volume Methods for Elliptic PDE's: A New Approach
We consider a new formulation for finite volume element methods, which is satisfied by known finite volume methods and it can be used to introduce new ones. This framework results by approximating the test function in the formulation of finite element method. We analyze piecewise linear conforming or nonconforming approximations on nonuniform triangulations and prove optimal order H1-norm and L2-norm error estimates.
Finite volume schemes for the p-laplacian on cartesian meshes
This paper is concerned with the finite volume approximation of the p-laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh’s interfaces is needed in order to discretize the p-laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally...
Finite volume schemes for the p-Laplacian on Cartesian meshes
This paper is concerned with the finite volume approximation of the p-Laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh's interfaces is needed in order to discretize the p-Laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally...
Finite-element discretizations of a two-dimensional grade-two fluid model
We propose and analyze several finite-element schemes for solving a grade-two fluid model, with a tangential boundary condition, in a two-dimensional polygon. The exact problem is split into a generalized Stokes problem and a transport equation, in such a way that it always has a solution without restriction on the shape of the domain and on the size of the data. The first scheme uses divergence-free discrete velocities and a centered discretization of the transport term, whereas the other schemes...
Finite-element discretizations of a two-dimensional grade-two fluid model
We propose and analyze several finite-element schemes for solving a grade-two fluid model, with a tangential boundary condition, in a two-dimensional polygon. The exact problem is split into a generalized Stokes problem and a transport equation, in such a way that it always has a solution without restriction on the shape of the domain and on the size of the data. The first scheme uses divergence-free discrete velocities and a centered discretization of the transport term, whereas the other schemes...
Formulations mixtes augmentées et applications
Formulations Mixtes Augmentées et Applications
We propose and analyse a abstract framework for augmented mixed formulations. We give a priori error estimate in the general case: conforming and nonconforming approximations with or without numerical integration. Finally, a posteriori error estimator is given. An example of stabilized formulation for Stokes problem is analysed.
Fractional order convergence rate estimates of finite difference method on nonuniform meshes.
Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems
Proper orthogonal decomposition (POD) is a powerful technique for model reduction of linear and non-linear systems. It is based on a Galerkin type discretization with basis elements created from the system itself. In this work, error estimates for Galerkin POD methods for linear elliptic, parameter-dependent systems are proved. The resulting error bounds depend on the number of POD basis functions and on the parameter grid that is used to generate the snapshots and to compute the POD basis. The...