The Computational Complexity of Elliptic Partial Differential Equations
In this paper, we consider the computational complexity of the class of all procedures for computing a second order accurate approximation (on a square grid) to the solution of a linear, second order elliptic partial differential equation in a square domain. In particular, we present and analyze a new asymptotically optimal procedure for this problem. Moreover, we will show that a preconditioned form of our procedure is well-conditioned.
KeywordsBasis Function Arithmetic Operation Mesh Point Elliptic Partial Differential Equation Finite Element Procedure
Unable to display preview. Download preview PDF.