We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd degree on T-meshes generated by the refinement strategy of Morgenstern and Peterseim (2015) in 2D and Morgenstern (2016) in 3D. Adaptivity is driven by some weighted residual a posteriori error estimator. We prove linear convergence of the error estimator (which is equivalent to the sum of energy error plus data oscillations) with optimal algebraic rates with respect to the number of elements of the underlying mesh.

我们考虑椭圆（可能是非对称）二阶偏微分方程的等几何分析（IGAFEM）的有限元方法的自适应算法。我们在2D中由Morgenstern和Peterseim（2015）在3D中通过Morgenstern和Peterseim（2015）的细化策略生成的T网格上采用任意奇数度的适合分析的T样条。适应性由一些加权残差后验误差估计器驱动。我们证明了误差估算器的线性收敛（等于能量误差加上数据振荡的总和）相对于底层网格元素的数量具有最佳代数率。