Search
Now showing items 1-10 of 10
Solving Laplacian problems with boundary singularities: A comparison of a singular function boundary integral method with the p/hp version of the finite element method
(2005)
We solve a Laplacian problem over an L-shaped domain using a singular function boundary integral method as well as the p/hp finite element method. In the former method, the solution is approximated by the leading terms of ...
Comparison of two methods for the computation of singular solutions in elliptic problems
(1997)
We compare two numerical methods for the solution of elliptic problems with boundary singularities. The first is the integrated singular basis function method (ISBFM), a finite-element method in which the solution is ...
On the effects of using curved elements in the approximation of the Reissner-Mindlin plate by the p version of the finite element method
(2003)
We consider the approximation of the Reissner-Mindlin plate model by the standard Galerkin p version finite element method. Under the assumption of sufficient smoothness on the solution, we illustrate that the method is ...
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. ...
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, ...
A note on p/hp finite element methods for reaction-diffusion problems in polygonal domains
(2000)
We present guidelines on how to choose the mesh and polynomial degree distribution for the approximation of reaction-diffusion problems in polygonal domains, in the context of the hp finite element method. These guidelines ...
Optimal mesh design for the finite element approximation of reaction-diffusion problems
(2002)
We consider the numerical approximation of singularly perturbed problems, and in particular reactiondiffusion problems, by the h version of the finite element method. We present guidelines on how to design non-uniform ...
Finite element computations for the Reissner-Mindlin plate model
(1998)
We consider the finite element (FE) approximation of the Reissner - Mindlin (RM) plate model, and indicate how to design meshes that yield accurate results when the p/hp version of the standard FE method is used. These ...
A p-version MITC finite element method for Reissner-Mindlin plates with curved boundaries
(2006)
We consider the approximation of Reissner-Mindlin plates with curved boundaries, using a p-version MITC finite element method. We describe in detail the formulation and implementation of the method, and emphasize the need ...
A numerical study on the finite element solution of singularly perturbed systems of reaction-diffusion problems
(2007)
We consider the approximation of singularly perturbed systems of reaction-diffusion problems, with the finite element method. The solution to such problems contains boundary layers which overlap and interact, and the ...