The lowest degree of polynomial for a finite element to solve a 2^th-order elliptic equation is k.The Morley element is such a finite element,of polynomial degree 2,for solving a fourth-order biharmonic equation.We de...The lowest degree of polynomial for a finite element to solve a 2^th-order elliptic equation is k.The Morley element is such a finite element,of polynomial degree 2,for solving a fourth-order biharmonic equation.We design a cubic H3-nonconforming macro-element on two-dimensional triangular grids,solving a sixth-order tri-harmonic equation.We also write down explicitly the 12 basis functions on each macro-element.A convergence theory is established and verified by numerical tests.展开更多
基金the National Natural Science Foundation of China(Nos.11271035,91430213,11421101).
文摘The lowest degree of polynomial for a finite element to solve a 2^th-order elliptic equation is k.The Morley element is such a finite element,of polynomial degree 2,for solving a fourth-order biharmonic equation.We design a cubic H3-nonconforming macro-element on two-dimensional triangular grids,solving a sixth-order tri-harmonic equation.We also write down explicitly the 12 basis functions on each macro-element.A convergence theory is established and verified by numerical tests.
