Mixed qualocation method for fourth order two-point boundary value problems
| Autor: | P. Devaraj, L. Jones Tarcius Doss, A. P. Nandini |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Piecewise linear function
symbols.namesake Exact solutions in general relativity Ordinary differential equation Mathematical analysis symbols Gaussian quadrature Gauss–Kronrod quadrature formula Finite element method Mathematics::Numerical Analysis Second derivative Mathematics Quadrature (mathematics) |
| Zdroj: | AIP Conference Proceedings. |
| ISSN: | 0094-243X |
| DOI: | 10.1063/1.4980890 |
| Popis: | A quadrature based mixed Petrov-Galerkin finite element method is applied to a fourth order linear non-homogeneous ordinary differential equation with variable coefficients. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by Gauss quadrature rule in the formulation itself. Optimal order apriori error estimates in W k,p-norms for k = 0, 1, 2 and 1 ≤ p ≤ ∞ are obtained without any restriction on the mesh, not only for the approximation of the exact solution also for its second derivative. These error estimates are validated by a suitable numerical example. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|