The New Computable Error Bounds In Finite Element For Possion's Equation

The finite element method is an effective numerical method for solving partial differential equations go with the developing of computer.It has been widely used in scientific and engineering computing. According to the error estimate,The truly error is unknow.P. Arbenz has proved that computable Error Bounds of the Poisson equation in the two-dimensional(n=2)is C₁ = 0.4888 (triangle linear element) or C₁ — 0.3184(rectangle bilinear element),but it is difficult to be generalized to the three-dimensional case.This paper we adopt "quadratic interpolation transition" to prove that C₁ = 0.4671+0(h^ε) (triagle linear element) and C₁ = 0.2886+0(h^ε) (rectangle bilinear element), further more,we find C₁ = 0.2982 + 0(h^ε) (three linear element) of the three-dimensional(n=3) for Poisson equa-tion.Where ε = , 1