Meshsize

Meshsize is a term used in mesh generation and numerical simulation to describe the resolution of a discretized domain. It represents the characteristic length of the mesh elements, often taken as the maximum edge length in a local region or, in a metric-based formulation, the target size specified by a size field. In two-dimensional meshes, this corresponds to the typical length of elements (for example, triangles); in three-dimensional meshes, to the edge lengths of tetrahedra or other polyhedra.

The meshsize controls a trade-off between accuracy and computational cost. Smaller meshsize yields finer resolution, better representation of geometric features and solution gradients, and generally higher accuracy, but increases the number of elements and the time and memory required by solvers. Conversely, a coarse meshsize reduces cost but may miss small features and degrade accuracy and convergence.

Meshsize is often chosen locally rather than globally. Meshing tools allow sizing fields or metrics to guide refinement, producing isotropic meshes with approximately equal edge lengths or anisotropic meshes where the target length varies by direction to align with solution features or geometry. Refinement is commonly driven by curvature, feature size, boundary layers, or error indicators.

In practice, meshsize is referred to as a local mesh size or characteristic length and is related to concepts such as the element size, minimum angle, and aspect ratio. It is a key parameter in finite element, finite volume, and isogeometric analyses, affecting stability, accuracy, and performance.