The p and hp finite element method for problems on thin domains

THE hp FINITE ELEMENT METHOD FOR SINGULARLYPERTURBED PROBLEMS IN SMOOTH

We consider the numerical approximation of singularly perturbed elliptic problems in smooth domains. The solution to such problems can be decomposed into a smooth part and a boundary layer part. We present guidelines for the eeective resolution of boundary layers in the context of the hp nite element method and we construct tensor product spaces that approximate these layers uniformly at a near...

The p and hp versions of the finite element method for problems with boundary layers

We study the uniform approximation of boundary layer functions exp(−x/d) for x ∈ (0, 1), d ∈ (0, 1], by the p and hp versions of the finite element method. For the p version (with fixed mesh), we prove super-exponential convergence in the range p+ 1/2 > e/(2d). We also establish, for this version, an overall convergence rate of O(p−1 √ lnp) in the energy norm error which is uniform in d, and sh...

A reduced constraint hp finite element method for shell problems

We propose and analyze an hp finite element method for the Nagdhi shell model, based on rectangular elements. We show that for the bending-dominated case, assuming sufficient smoothness on the solution, the method is locking free in terms of both h and p, as the thickness of the shell tends to zero. Our results are established under the assumption that the geometrical coefficients appearing in ...

Hp Finite Element Method for Convection-diiusion Problems

On the hp Finite Element Method for Singularly Perturbed Two-Point Boundary Value Problems

In this work, a singularly perturbed two-point boundary value problem of convection-diiusion type is considered. A hp version nite element method on a strongly graded piecewise uniform mesh of Shishkin type is used to solve the model problem. With the analytic assumption of the input data, it is shown that the method converges exponentially and the convergence is uniformly valid with respect to...