Analysis of Galerkin and streamline-diffusion FEMs on piecewise equidistant meshes for turning point problems exhibiting an interior layer
Copyright policy )Analysis of Galerkin and streamline-diffusion FEMs on piecewise equidistant meshes for turning point problems exhibiting an interior layer
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 $\varepsilon$ are proven in the energy norm and in the stronger SDFEM-norm, respectively. Numerical experiments confirm the theoretical findings.
18 pages, 5 figures
- TU Dresden Germany
Numerical solution of boundary value problems involving ordinary differential equations, boundary value problems, higher order, Numerical Analysis (math.NA), turning point, layer-adapted meshes, 65L11, 65L20, 65L50, 65L60, interior layer, streamline-diffusion finite element method, error estimates, Singular perturbations for ordinary differential equations, Mesh generation, refinement, and adaptive methods for ordinary differential equations, FOS: Mathematics, Linear boundary value problems for ordinary differential equations, Mathematics - Numerical Analysis, numerical experiments, singular perturbation, Numerical solution of singularly perturbed problems involving ordinary differential equations, Error bounds for numerical methods for ordinary differential equations
Numerical solution of boundary value problems involving ordinary differential equations, boundary value problems, higher order, Numerical Analysis (math.NA), turning point, layer-adapted meshes, 65L11, 65L20, 65L50, 65L60, interior layer, streamline-diffusion finite element method, error estimates, Singular perturbations for ordinary differential equations, Mesh generation, refinement, and adaptive methods for ordinary differential equations, FOS: Mathematics, Linear boundary value problems for ordinary differential equations, Mathematics - Numerical Analysis, numerical experiments, singular perturbation, Numerical solution of singularly perturbed problems involving ordinary differential equations, Error bounds for numerical methods for ordinary differential equations
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).5 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!