A mass-conservative high-order unfitted finite element method for convection–diffusion equations in evolving domains is proposed. The space–time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307 (2016)] is extended to naturally achieve mass conservation by utilizing Reynolds’ transport theorem. Furthermore, by partitioning the time-dependent domain into macroelements, a more efficient stabilization procedure for the cut finite element method in time-dependent domains is presented. Numerical experiments illustrate that the method fulfills mass conservation, attains high-order convergence, and the condition number of the resulting system matrix is controlled while sparsity is increased. Problems in bulk domains as well as coupled bulk-surface problems are considered.

中文翻译：

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求解瞬态域问题的高阶保守切割有限元方法


提出了一种用于演化域中对流扩散方程的质量守恒高阶不拟合有限元方法。时空方法在[P. Hansbo、MG Larson、S. Zahedi，计算机。方法应用机甲。工程。 307 (2016)] 被扩展以利用雷诺输运定理自然地实现质量守恒。此外，通过将时变域划分为宏单元，提出了时变域中切割有限元法的更有效的稳定程序。数值实验表明，该方法满足质量守恒，达到高阶收敛，在提高稀疏性的同时控制了所得系统矩阵的条件数。考虑了体域中的问题以及耦合体表面问题。