Finite difference approximation to the Cauchy problem for non-linear parabolic differential equations
Finite difference methods for coupled flow interaction transport models.
Finite element analysis of primal and dual variational formulations of semicoercive elliptic problems with nonhomogeneous obstacles on the boundary
The Poisson equation with non-homogeneous unilateral condition on the boundary is solved by means of finite elements. The primal variational problem is approximated on the basis of linear triangular elements, and -convergence is proved provided the exact solution is regular enough. For the dual problem piecewise linear divergence-free approximations are employed and -convergence proved for a regular solution. Some a posteriori error estimates are also presented.
Finite element approximation of a free boundary problem arising in the theory of liquid drops ans plasma physics
Finite element approximation of a model reaction - diffusion problem with a non-Lipschitz nonlinearity.
Finite element approximation of a periodic Ginzburg-Landau model for type-II superconductors.
Finite element approximation of nonlinear elliptic problems with discontinuous coefficients
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...