𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A hybrid difference scheme on a Shishkin mesh for linear convection–diffusion problems

✍ Scribed by Torsten Linß; Martin Stynes


Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
228 KB
Volume
31
Category
Article
ISSN
0168-9274

No coin nor oath required. For personal study only.


📜 SIMILAR VOLUMES


An upwind difference scheme on a novel S
✍ Torsten Linß 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 110 KB

We consider an upwind ÿnite di erence scheme on a novel layer-adapted mesh (a modiÿcation of Shishkin's piecewise uniform mesh) for a model singularly perturbed convection-di usion problem in two dimensions. We prove that the upwind scheme on the modiÿed Shishkin mesh is ÿrst-order convergent in the

Numerical methods on Shishkin meshes for
✍ Torsten Linß; Martin Stynes 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 803 KB

On the unit square, we consider a model singularly perturbed convection±diusion problem whose solution contains exponential boundary and corner layers. Shishkin meshes are frequently used to solve such problems numerically. We compare and evaluate the performance of several numerical methods on thes

A Uniformly Convergent Galerkin Method o
✍ Martin Stynes; Eugene O'Riordan 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 240 KB

A Galerkin finite element method that uses piecewise bilinears on a simple piecewise equidistant mesh is applied to a linear convection-dominated convection-diffusion problem in two dimensions. The method is shown to be convergent, uniformly in the perturbation parameter, of order N y1 ln N in a glo

Continuous interior penalty method on a
✍ S. Franz 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 239 KB

The continuous interior penalty (CIP) method for elliptic convection-diffusion problems with characteristic layers on a Shishkin mesh is analysed. The method penalises jumps of the normal derivative across interior edges. We show that it is of the same order of convergence as the streamline diffusio

Pointwise convergence of approximations
✍ Wim Lenferink 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 140 KB

A centered difference or finite element discretization is applied to a singularly perturbed, one-dimensional boundary value problem. The discretization uses a piecewise equidistant mesh. It is proved that the pointwise error is (almost) of second order with respect to the number of nodes, uniformly