Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation interpolates nonlinear terms onto the finite element approximation space, we propose the use of a separate approximation space that is tailored to the nonlinearity. In many cases, this allows for the exact reformulation of the discrete nonlinear problem into a quadratic problem with algebraic constraints. Furthermore, the substitution of the nonlinear terms often shifts general nonlinear forms into trilinear forms, which can easily be described by third-order tensors. The numerical benefits as well as the advantages in comparison to the original group finite element method are studied using a wide variety of academic benchmark problems.

中文翻译：

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扩展群有限元法

非线性有限元离散化的插值方法通常用于消除与非线性系统重复组装相关的计算成本。虽然群有限元公式将非线性项插入到有限元近似空间中，但我们建议使用针对非线性度量身定制的单独近似空间。在许多情况下，这允许将离散非线性问题精确地重新表述为具有代数约束的二次问题。此外，非线性项的代换常常将一般非线性形式转变为三线性形式，这可以很容易地用三阶张量来描述。