【摘要】 就一类典型的抛物型问题——热传导方程,研究矩形网格上质量集中有限元方法的有关性质.首先给出了矩形单元上双线性有限元基函数的积分公式,在此基础上讨论质量集中有限元方法的误差估计.研究表明,矩形网格上的质量集中有限元方法具有与普通的有限元方法同等的逼近精度,但却具有更少的计算量,并且在一定条件下可以保持极值性质.最后给出了在矩形网格上质量集中有限元方法保持极值性质的剖分条件.更多还原

【Abstract】 The property of the lumped mass finite element method(LMFEM) on rectangular mesh is investigated to solve a typical parabolic problem,i.e.,the heat transfer equation.The integral formula of the bi-linear finite element basis function on the rectangular mesh is given to discuss the error estimation for LMFEM.It is found that LMFEM has the equivalent approximate accuracy to the standard finite element method on the rectangular mesh,while the former has less computational cost and can retain the maximum principle under certain conditions.Moreover,the partitioning conditions for retaining the maximum principle on rectangular mesh are given.更多还原