An analysis of a singularly perturbed two-point boundary value problem using only finite element techniques
نویسندگان
چکیده
منابع مشابه
Two-point Boundary Value Problem Using Only Finite Element Techniques
We give a new analysis of Petrov-Galerkin finite element methods for solving linear singularly perturbed two-point boundary value problems without turning points. No use is made of finite difference methodology such as discrete maximum principles, nor of asymptotic expansions. On meshes which are either arbitrary or slightly restricted, we derive energy norm and L norm error bounds. These bound...
متن کاملA Finite Difference Technique for Singularly Perturbed Two-Point Boundary value Problem using Deviating Argument
In this paper, we have presented a finite difference technique to solve singularly perturbed two-point boundary value problem using deviating argument. We have replaced the given second order boundary value problem by an asymptotically equivalent first order differential equation with deviating argument. We have applied a fourth order finite difference approximation for the first derivative and...
متن کاملAn Ε-uniform Finite Element Method for Singularly Perturbed Two-point Boundary Value Problems
This work develops an ε-uniform finite element method for singularly perturbed two-point boundary value problems. A surprising and remarkable observation is illustrated: By inserting one node arbitrarily in any element, the new finite element solution always intersects with the original one at fixed points, and the errors at those points converge at the same rate as regular boundary value probl...
متن کاملOn 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...
متن کاملNumerical solution of a singularly perturbed two-point boundary-value problem using collocation
In this paper we study a class of numerical methods to solve a singularly perturbed two-point boundary value problem. Our schemes arise as result of choosing an appropriate basis for the solution, as well as making use of collocation. It is possible to obtain arbitrarily high-order methods. We note that, in some cases (constant coefficients), we obtain the exact solution. Particular attention i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1991
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1991-1068809-4