Optimality of grids based on a combined r-h adaptive strategy

A critical review of earlier works on optimality of finite element grids has been made. A material force method of r-adaption to obtain optimal initial grids has been described. The study focuses on determining the configurational driving force and its convergence rate across an interior patch node for one-dimensional linear, quadratic element and two-dimensional bilinear quadrilateral elements. Numerical implementation is made on one and two-dimensional problems. Various aspects considered to define optimality in earlier works along with their predefined guidelines have also been worked out with some modifications for the material force method and it is shown that this method of adaption provides good optimal grids. The method is advantageous owing to its physical basis and mathematical vigor than earlier works. Based on the numerical studies conducted a combined adaptive strategy incorporating node disposition and mesh enrichment has been evolved to obtain an optimal mesh for a specified accuracy