Analysis of Galerkin and streamline-diffusion FEMs on piecewise equidistant meshes for turning point problems exhibiting an interior layer

Abstract

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 equidistant meshes proposed by Sun and Stynes. We also study the streamline-diffusion finite element method (SDFEM) for such problems. For these methods error estimates uniform with respect to $\epsilon$ are proven in the energy norm and in the stronger SDFEM-norm, respectively. Numerical experiments confirm the theoretical findings.

18 pages, 5 figures

References in corpus (1)

• Uniform error estimates for general semilinear turning point problems on layer-adapted meshes

Cited by in corpus (1)

• Uniform error estimates for general semilinear turning point problems on layer-adapted meshes