Discrete Mixed Petrov-Galerkin Finite Element Method for a Fourth-Order Two-Point Boundary Value Problem

Abstract EN

A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation.

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 the Gauss quadrature rule in the formulation itself.

Optimal order a priori error estimates are obtained without any restriction on the mesh.