Sparse Tensor Product Wavelet Approximation of Singular Functions

Abstract. On product domains, sparse-grid approximation yields optimal, dimension-independent convergence rates when the function that is approximated has L2-bounded mixed derivatives of a sufficiently high order. We show that the solution of Poisson's equation on the n-dimensional hypercube with Dirichlet boundary conditions and smooth right-hand side generally does not satisfy this condition. As suggested by P.-A. Nitsche in [Constr. Approx., 21 (2005), pp. 63

• Type: Journal
• Year: 2010
• Where: SIAMMA
• Authors: Monique Dauge, Rob Stevenson
• Keywords: Dimension-independent Convergence Rate, Regularity Conditions, SIAMMA 2010, Sparse-grid Approximation