finite element approximation meaning in English
有限单元近似解
Examples
- Based on this fomulation , expanded mixed finite element approximations of the hyperbolic problems are considered . optimal order error estimates for the scalar unknwon , its gradient and its flux in l2 - norms are obtained for this new mixed formulation
给出了逼近未知函数、未知函数梯度和流体流量的最优l ~ 2模误差估计以及拟最优的最大模误差估计。 - Its biquadratic finite element approximation is considered and under the appropriately graded meshes , quasi - optimal order error estimates in the - weighted h ^ 1 - norm , up to a logarithmic factor in the singular perturbation parameter , are proved
然后，考虑此方程在分层网格剖分上的双二次有限元逼近，在-加权h ^ 1 -模意义下得到了至多相差一个关于摄动参数对数因子的拟最优阶收敛的误差估计。 - On the basis of some conclusion , we have proved that the schemes have second - order convergence accuracy for the time discretization , a two - level method for resolving the nonlinearity in finite element approximation of the stationary conduction - convection problems is presented
在某些已有结论的基础之上，我们证明了这种格式对于时间离散上的二阶精度。提出了一种解决定常的热传导-对流问题的有限元近似中出现的非线性问题的两层方法。 - In this paper , based on an improved orthogonal expansion in an clement , using the new idea of ref . [ 3 ] , a new error expression of n - degree hermite finite element approximation to one - dimensional 4 - degrec 2 - point bounded problem and 2 - degree ordinary differential problem , and then optimal order superconvergence for their first derivatives is obtained . moreover , we get the same result of their optimal order superconvergence
本文针对在改进的单元正交性估计的基础上，利用文[ 3 ]提出的新想法，得到一维四阶两点边值问题和二阶常微初值问题的n次赫米特有限元u _ h c ~ 1的新误差估计式，以及导数误差的最佳阶超收敛，并且两者有相同的超收敛结果。 - In view of the model problem , we do some analysis for the approximations respectively ; we compare uh with the standard finite element approximation of u in vh , and ph with the usual ( non - least - squares ) mixed finite element approximation of p , provided of course that the same approximating spaces are used . it turns out that under weak conditions , they are " almost " equal , i . e . , higher order perturbations of each other . apart from improved a priori bounds , the result also gives us the possibility to extend superconvergence results from the standard and mixed method to the least - squares mixed method
针对模型问题，我们引进对偶问题进行收敛性分析，最小二乘混合元解u _ h与标准有限元解比较，而p _ h则与通常意义下的混合元解比较，结果证明在比较弱的正则性假设条件下，最小二乘混合有限元解u _ h ， p _ h标准有限元解u _ h ~ s和混合元解p _ h ~ m的高阶扰动。