A double -shaped bifurcation curve for a reaction-diffusion model with nonlinear boundary conditions.
A doubly degenerate elliptic system
A duality theorem for solutions of elliptic equations.
A family of finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
A family of sixth-order compact finite-difference schemes for the three-dimensional Poisson equation.
A fast solver for the first biharmonic boundary value problem.
A FETI-DP preconditioner for mortar methods in three dimensions.
A few results about the -Laplace's operator.
A few symmetry results for nonlinear elliptic PDE on noncompact manifolds
A fibering map approach to a semilinear elliptic boundary value problem.
A fibering method approach to a system of quasilinear equations with nonlinear boundary conditions
We provide an existence result for a system of quasilinear equations subject to nonlinear boundary conditions on a bounded domain by using the fibering method.
A Finite Eement Scheme for Domains with Corners.
A Finite Element - Capacitane Method for Elliptic Problems on Regions Partitioned into Subregions.
A Finite Element Merthod Scheme for one Dimensional Elliptic Equations with High Super Convergence at the Nodes.
A finite element method for domain decomposition with non-matching grids
In this note, we propose and analyse a method for handling interfaces between non-matching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson’s equation as a model. A priori and a posteriori error estimates are given. Some numerical results are included.
A finite element method for domain decomposition with non-matching grids
In this note, we propose and analyse a method for handling interfaces between non-matching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson's equation as a model. A priori and a posteriori error estimates are given. Some numerical results are included.
A finite element method for exterior interface problems.
A finite element method on composite grids based on Nitsche’s method
In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.
A finite element method on composite grids based on Nitsche's method
In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.
A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids
We present a finite volume method based on the integration of the Laplace equation on both the cells of a primal almost arbitrary two-dimensional mesh and those of a dual mesh obtained by joining the centers of the cells of the primal mesh. The key ingredient is the definition of discrete gradient and divergence operators verifying a discrete Green formula. This method generalizes an existing finite volume method that requires “Voronoi-type” meshes. We show the equivalence of this finite volume...