Abstract
We propose a simple polynomial basis-set that is easily extendable to any desired higher-order accuracy. This method, i. e. the CIP-BS method, is based on the Constrained Interpolation Profile (CIP) method and the profile is chosen so that the subgrid scale solution approaches the real solution with the constraints from the spatial derivative of the original equation. Thus the solution even on the subgrid scale becomes consistent with the master equation. By increasing the order of the polynomial, this solution quickly converges. The governing equation is transformed into the discretized form by taking scalar products with each basis function.
