High-order accuracy approximation for the two-point boundary value problem of the fourth order with degenerate coefficients

Abstract

The paper deals with the construction of high-order accuracy finite element schemes for the fourth-order ordinary differential equation with degenerate coefficients on the boundary. The method for solving the problem is based on both multiplicative and additive-multiplicative separation of singularities. For the given class of smoothness of the right-hand sides, the optimal convergence rate has been proved.

Keywords

• two-point boundary value problem
• finite element schemes
• weight function space
• multiplicative decomposition of singularity
• additive-multiplicative decomposition of singularity