有限元法的收敛性条件及误差公式
Convergence and Error Formula for Finite Element Method
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摘要: 基于变分法中的可动边界变分理论,建立了有关非协调元与细分网格的有限元最佳剖分变分原理。由此原理可以求得有限元法的收敛条件和在元素交界处的误差计算公式。根据误差计算公式,可建立更有成效的自适应有限元法与边界元法的程序系统。Abstract: Based on variational problem of variable boundary in calculus of variation, we have established the vatiational principles of optimum subdivision for non-conforming element and subdivision grid. We can obtain convergence conditions and error formula at interfaces between elements for finite element method with this variational principles. Based on error formula, a more dffective programme system can be established for adaptive procedures of finite element and boundary element methods.