Solving PDEs With Variable Coefficients on Locally Adaptive Sparse Grids and Corresponding Refinement Strategies - Scherner-Grießhammer, Riccarda; Pflaum, Christoph (Lecture Notes in Computational Science and Engineering, 2025)
Using sparse grids and the L2-orthogonality of prewavelets, one can apply a Ritz-Galerkin discretization of elliptic partial differential equations (PDEs) with variable coefficients even for dimension d>3. This leads to a linear equation system with O(N(log(N)d-1)) unknowns. The theory of regular sparse grids can be extended to locally adaptive sparse grids. These are needed for several applications like PDEs with corner singularities or the high-dimensional Schrödinger equation. We introduce two different refinement strategies to obtain locally adaptive sparse grids. A numerical example shows how the correct choice of such a refinement strategy has major impact on the convergence rate of the discretization.
CRIS-Team Scopus Importer:2025-05-23