Complexity Bounds for Regular Finite Difference and Finite Element Grids
Alan J. Hoffman, Michael S. Martin, Donald J. Rose · SIAM Journal on Numerical Analysis · 1973
Sharp lower bounds are obtained for multiplications and storage in the sparse system arising from the application of finite difference or finite element techniques to linear boundary value problems on plane regions yielding regular $n \times n$ grids. Graph-theoretic techniques are used to take advantage of the simplicity of the underlying combinatorial structure of the problem.