中文摘要：

采用节点有限元方法求解节点位函数的精度较高,但基于节点位函数值在单元内求梯度计算场强的方法误差较大。为了提高由已知节点电位求解场强的计算精度,该文提出了一种全域求解节点场强的方法。该方法基于面矢量基函数,对电位的梯度方程进行离散,得到以全域场强为未知量,以节点电位为已知量的有限元方程。通过求解得到全域节点上的场强,充分利用了电位的整体分布信息,比在局部计算电位梯度获得场强的方法精度要高。在形成有限元方程过程中,对梯度项进行了转换处理,避免了求解电位梯度运算,直接利用节点电位值,从而完全克服了在局部区域计算电位梯度所带来的误差,有效提高了场强求解精度。所提方法不仅适用于静电场问题,也适用于其他已知场的标量位分布,求解矢量场强分布的问题。

英文摘要：

By using nodal FEM, nodal potential values are obtained accurately, but using accurate nodal potential values cannot obtain the same accurate field intensity value. In order to improve field intensity precision calculated by known potentials, this paper presents a global solving method. This method could obtain FEM equations by discretizing electric potential gradient equation, based on facial vector basis functions. Taking advantage of global distribution information of electric potential, this method could enhance field intensity precision and get more accurate solution than the local element post processing method. During derivation of FEM equations, gradient operation of discrete potentials is avoided, which could dramatically improve field intensity precision and totally overcome the error of local element post processing method. The new method could not only be used in static electric field evaluation problem, but also in other vector field value calculation problems based on known potential values.