Splitting extrapolation for solving second order elliptic systems with curved boundary in R d by using d-quadratic isoparametric finite element Original Research Article

Splitting extrapolation for solving second order elliptic systems with curved boundary in View the MathML source by using isoparametric d-quadratic element Q2 is presented, which is a new technique for solving large scale scientific and engineering problems in parallel. By means of domain decomposition, a large scale multidimensional problem with curved boundary is turned into many discrete problems involving several grid parameters. The multivariate asymptotic expansions of isoparametric d-quadratic Q2 finite element errors with respect to independent grid parameters are proved for second order elliptic systems. Therefore after solving smaller problems with similar sizes in parallel, a global fine grid approximation with higher accuracy is computed by the splitting extrapolation method.