相关论文: Analysis of SDFEM on Shishkin triangular meshes an…

In this paper, we analyze the supercloseness property of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes, which is different from one in the case of rectangular meshes. The analysis depends on integral…

We consider a singularly perturbed convection-diffusion with exponential and characteristic boundary layers. The problem is numerically solved by the FEM and SDFEM method with bilinear elements on a graded mesh. For the FEM we prove almost…

In this technical report, we present estimations of the discrete Green's function of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes for singularly perturbed problems with characteristic layers.

We propose some useful estimates for the pointwise error estimates of the streamline diffusion finite element method (SDFEM) on Shishkin meshes, when SDFEM is applied for problems of characteristic layers.

In this technical report, we present estimations of the discrete Green's function of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes for problems with only exponential layers.

In this paper we consider a model singularly perturbed convection diffusion problem which is solved by a streamline diffusion finite element method (SDFEM) on a Shishkin rectangular mesh. To put insight into the influences of stabilization…

We propose estimates of the discrete Green function for the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes.

We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted piecewise…

Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…

We propose the estimates of the discrete Green function for the stream- line diffusion finite element method (SDFEM) on Shishkin meshes.

For singularly perturbed convection-diffusion problems, supercloseness analysis of finite element method is still open on Bakhvalov-type meshes, especially in the case of 2D. The difficulties arise from the width of the mesh in the layer…

This paper presents the first analysis of parameter-uniform convergence for a hybridizable discontinuous Galerkin (HDG) method applied to a singularly perturbed convection-diffusion problem in 2D using a Shishkin mesh. The primary…

We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…

In this article, a parameter-uniform numerical method is presented to solve one-dimensional singularly perturbed parabolic convection-diffusion turning point problem exhibiting two exponential boundary layers. We study the asymptotic…

We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…

On Bakhvalov-type mesh, uniform convergence analysis of finite element method for a 2-D singularly perturbed convection-diffusion problem with exponential layers is still an open problem. Previous attempts have been unsuccessful. The…

This paper investigates the supercloseness of a singularly perturbed convection diffusion problem using the direct discontinuous Galerkin (DDG) method on a Shishkin mesh. The main technical difficulties lie in controlling the diffusion term…

Consider a singularly perturbed convection-diffusion problem with small, variable diffusion. Based on certain a priori estimates for the solution we prove robustness of a finite element method on a Duran-Shishkin mesh.

For convection dominated problems, the streamline upwind Petrov--Galerkin method (SUPG), also named streamline diffusion finite element method (SDFEM), ensures a stable finite element solution. Based on robust a posteriori error estimators,…

A nonsymmetric discontinuous Galerkin FEM with interior penalties has been applied to one-dimensional singularly perturbed reaction-diffusion problems. Using higher order splines on Shishkin-type layer-adapted meshes and certain graded…