High-Order Accuracy Approximation for a Two-Point Boundary Value Problem of Fourth Order with Degenerate Coefficients

Resumo

High-order accurate finite element schemes for a fourth-order ordinary differential equation with degenerate coefficients on the boundary are constructed. The method for solving the problem is based on multiplicative and additive-multiplicative separation of singularities. For right-hand sides of the given class of smoothness, an optimal convergence rate is proved.