Browsing by Subject "Singularly perturbed problem"
Now showing items 1-6 of 6
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Finite element analysis of an exponentially graded mesh for singularly perturbed problems
(2015)We present the mathematical analysis for the convergence of an h version Finite Element Method (FEM) with piecewise polynomials of degree p ≥ 1, defined on an exponentially graded mesh. The analysis is presented for a ...
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Article
An hp finite element method for a 4th order singularly perturbed boundary value problem in two dimensions
(2017)We consider a fourth order singularly perturbed boundary value problem posed in a square and the approximation of its solution by the hp version of the finite element method on the so-called Spectral Boundary Layer mesh. ...
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Article
The hp finite element method for problems in mechanics with boundary layers
(1998)Boundary layer phenomena are well-known in the study of fluid flow problems. Perhaps less known, but equally ubiquitous, is their existence in thermal, plate and shell analysis, where they also play a very significant role. ...
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A note on the convergence rate of the finite element method for singularly perturbed problems using the Shishkin mesh
(2003)We consider the numerical approximation of singularly perturbed problems by the h version of the finite element method on a piecewise uniform, Shishkin mesh. It is well known that this method yields uniform approximations, ...
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Article
A Parameter Robust Finite Element Method for Fourth Order Singularly Perturbed Problems
(2017)We consider fourth order singularly perturbed problems in one-dimension and the approximation of their solution by the h version of the finite element method. In particular, we use piecewise Hermite polynomials of degree ...
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Uniform approximation of singularly perturbed reaction-diffusion problems by the finite element method on a Shishkin mesh
(2003)We consider the numerical approximation of singularly perturbed reaction-diffusion problems over two-dimensional domains with smooth boundary. Using the h version of the finite element method over appropriately designed ...