Tensor Spaces and Numerical Tensor Calculus pp 463-472 | Cite as

# Applications to Elliptic Partial Differential Equations

## Abstract

We consider elliptic partial differential equations in *d* variables and their discretisation in a product grid \(\mathbf{I} = \times^{d}_{j=1}I_{j}\). The solution of the discrete system is a grid function, which can directly be viewed as a tensor in \(\mathbf{V} = {\bigotimes}^{d}_{j=1}\mathbb{K}^{I_{j}}\). In *Sect. 16.1* we compare the standard strategy of local refinement with the tensor approach involving regular grids. It turns out that the tensor approach can be more efficient. In *Sect. 16.2* the solution of boundary value problems is discussed. A related problem is the eigenvalue problem discussed in *Sect. 16.3*.

We concentrate ourselves to elliptic boundary value problems of second order. However, elliptic boundary value problems of higher order or parabolic problems lead to similar results.

## Keywords

Eigenvalue Problem Uniform Grid Elliptic Boundary Elliptic Partial Differential Equation Tensor Format## Preview

Unable to display preview. Download preview PDF.