Modified nodal cubic spline collocation for biharmonic equations
The authors formulate a mixed approach with a modified cubic spline collocation scheme in order to solve the biharmonic Dirichlet problem on a rectangle. They prove the existence and the uniqueness of the solution and show how the scheme can be solved at a low cost. The scheme produces fourth order approximation for the solution, in the global maximum norm, and the same order for the partial derivatives of the solution in the partition nodes. Two test problems are solved in order to underline the qualities of the method.
preconditioned conjugate gradient method
scientific article; zbMATH DE number 5145104
scientific article