Encontrados 9 documentos, a visualizar página 1 de 1
Supraconvergent cell-centered scheme for two dimensional elliptic problems
Barbeiro, S.In this paper we study the convergence properties of a cell-centered finite difference scheme for second order elliptic equations with variable coefficients subject to Dirichlet boundary conditions. We prove that the finite difference scheme on nonuniform meshes although not even being consistent are nevertheless second order convergent. More precisely, second order convergence with respect to a discrete versio...
Coupled vehicle-skin models for drug release
Barbeiro, S.; Ferreira, J. A.http://www.sciencedirect.com/science/article/B6V29-4VM43XG-1/2/493993c9687e5ff240f132118604a862
H1-second order convergent estimates for non Fickian models
Barbeiro, S.; Ferreira, J. A.; Pinto, L.In this paper we study numerical methods for integro-differential initial boundary value problems that arise, naturally, in many applications such as heat conduction in materials with memory, diffusion in polymers and diffusion in porous media. We propose finite difference methods to compute approximations for the continuous solutions of such problems. For those methods we analyze the stability and study the co...
Integro-differential models for percutaneous drug absorption
Barbeiro, S.; Ferreira, J. A.In this paper we propose new mathematical models for percutaneous absorption of a drug. The new models are established by introducing, in the classical Fick's law, a memory term being the advection–diffusion equations of the classical models replaced by integro-differential equations. The well-posedness of the models is studied with Dirichlet, Neumann and natural boundary conditions. Methods for the computation...
Discrete negative norms in the analysis of supraconvergent two dimensional cell...
Barbeiro, S.In this paper we study the convergence properties of cell-centered finite difference schemes for second order elliptic equations with variable coefficients. We prove that the finite difference schemes on nonuniform meshes although not even being consistent are nevertheless second order convergent. The convergence is studied with the aid of an appropriate negative norm. Numerical examples support the convergence...
Discretely compact imbeddings in spaces of cell-centered grid functions
Barbeiro, S.Compactness of imbeddings in discrete counterparts of Sobolev spaces is considered. We study the imbeddings in spaces of cell-centered grid functions, in one and two dimensional domains. No restrictions are made on the mesh-ratios of the underlying meshes.
A superconvergent linear FE approximation for the solution of an elliptic syste...
Barbeiro, S.; Ferreira, J. A.The aim of this work is to study a nonstandard piecewise linear finite element method for elliptic systems of partial differential equations. This nonstandard method was considered by the authors for scalar elliptic equations and for a planar elasticity problem. The method enables us to compute a superconvergent numerical approximation to the solution of the system of partial differential equations. ; http:/...
Superconvergence of Piecewise Linear Semi-Discretizations for Parabolic Equatio...
Barbeiro, S.; Ferreira, J. A.; Brandts, J.In this paper we study the convergence properties of semi-discrete approximations for parabolic problems defined on two dimensional polygonal domains. These approximations are constructed using a nonstandard piecewise linear finite element method based on nonuniform triangulations of the domain and considering a variational formulation with a sesquilinear form which can be no strongly coercive. In order to incr...
A nonstandard linear finite element method for a planar elasticity problem
Barbeiro, S.; Ferreira, J. A.The aim of this work is to present a nonstandard linear finite element method for a planar elasticity problem. The error for the solution computed with this method is estimated with respect to H1×H1-norm and second-order convergence is shown. ; http://www.sciencedirect.com/science/article/B6TYD-42MFD5J-5/1/b7fb435ba1f05aa7afa768ee9308a46a
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