Anisotropic mesh adaptation for continuous finite element discretization through mesh optimization via error sampling and synthesis

•DOF efficiency of Continuous FEM realized in adaptive context.•Optimal mesh anisotropy demonstrated for CG.•Nodal error models exploit continuity of basis functions.•Algorithm uses edge–based local solve patches. 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 L2 projection and linear advection diffusion.