Discretization of elliptic differential equations on curvilinear bounded domains with sparse grids (Q1913347)

The authors consider the approximation of the weak solutions of some linear elliptic partial differential equation using finite elements on sparse grids. They construct some sparse grid finite element spaces, an interpolation theory on sparse grids and a discretization algorithm for sparse grids using grid generation by transformation. They take into acocunt curvilinear bounded domains. The numerical results for some examples show a very good convergence in the discrete \(L^2\) norm although the boundary of the domain has a ``bad'' shape (reentrant corners, for example).