Convergence analysis of orthogonal spline collocation for elliptic boundary value problems

Existence, uniqueness, and optimal order H-2, H-1, and L-2 error bounds are established for the orthogonal spline collocation solution of a Dirichlet boundary value problem on the unit square. The linear, elliptic, nonself-adjoint, partial differential equation is given in nondivergence form. The approximate solution, which is a tensor product of continuously differentiable piecewise polynomials of degree r greater than or equal to 3, is determined by satisfying the partial differential equation at the nodes of a composite Gauss quadrature.