Anisotropic output-based mesh adaptivity is a powerful technique for controlling the output error of finite element simulations, particularly when used in conjunction with higher-order discretization. The Mesh Optimization via Error Sampling and Synthesis (MOESS) algorithm makes use of the continuous mesh model which encodes local mesh sizing and anisotropy in a Riemannian metric field, and was developed for Discontinuous Galerkin (DG) discretization. In this paper, we outline an extension of the MOESS algorithm for discretizations which are defined by basis functions that are continuous across element boundaries. Error models are defined in terms of local error estimates defined at vertices, and local solutions are computed on local patches defined in terms of the edges of the mesh. The resulting algorithm displays reduced error for the same number of degrees of freedom compared to the MOESS algorithm for DG discretization, as illustrated by some numerical examples for $L^2$ projection and linear advection diffusion.

基于各向异性输出的网格自适应性是一种用于控制有限元模拟输出误差的强大技术，尤其是在与高阶离散化结合使用时。通过误差采样和综合（MOESS）算法进行的网格优化利用了连续网格模型它在黎曼度量域中编码局部网格大小和各向异性，并且是为不连续Galerkin（DG）离散化开发的。在本文中，我们概述了用于离散化的MOESS算法的扩展，该离散化由基本函数定义，该基本函数跨元素边界连续。误差模型是根据在顶点处定义的局部误差估计来定义的，而局部解是根据根据网格的边缘定义的局部补丁来计算的。与用于DG离散化的MOESS算法相比，在相同数量的自由度下，所得算法显示出减少的误差，如针对${\mathrm{大号}}^2$ 投影和线性对流扩散。