Biorthogonal wavelet approximation methods for the heat equation
Christian Bourgeois, Serge Nicaise · Birkhäuser Basel eBooks · 2001
We consider the integral formulation of the heat equation in a smooth domain of ℝ2 with Dirichlet and Neumann boundary conditions. The unknown solutions of the integral equations belong to anisotropic Sobolev spaces and are approximated by the Galerkin method using an appropriate wavelet basis. This allows to compress the stiffness matrix from O(N 2) to O(N), and to obtain a uniformly bounded condition number. Finally, we show that the compressed scheme converges as fast as the Galerkin method based on B-splines basis.