Manufacturing & engineering
Mesh convergence
Definition
Mesh convergence is the process of refining a finite element mesh and checking whether a chosen result approaches a stable value. It demonstrates that the reported quantity is becoming insensitive to element size or approximation order, but it does not validate the loads, constraints, materials, contacts, or other modelling assumptions.
Also known as: mesh independence, mesh convergence study, grid convergence, discretisation convergence
Updated
What changes between runs#
In an h-refinement study, the analyst reduces element size in the region of interest and resolves the same model. In a p-refinement study, the solver increases the polynomial order of the element approximation. SOLIDWORKS Simulation Tutorials 2026 demonstrates both adaptive approaches and their convergence graphs.
Loads, boundary conditions, materials, contacts, geometry, solver options, and result locations should remain fixed during the series. Changing those inputs at the same time prevents the analyst from separating discretisation error from a different model.
What to compare#
NAFEMS recommends plotting a critical result parameter at a specific location against mesh density, normally using at least three runs. Displacement, reaction force, strain energy, path stress, or stress at a stable named location may be more useful than the model's single largest nodal stress.
The acceptable change depends on the engineering decision, governing code, and consequence of error. There is no universal element size that makes unrelated models converged.
Limits#
Mesh convergence verifies one part of a numerical model. It does not prove that the geometry, loads, restraints, material law, contact behaviour, or failure criterion represents the physical component correctly.
A peak at a point load or ideal sharp corner may increase without limit as the mesh is refined. That pattern indicates a possible stress singularity, which needs separate treatment rather than a finer global mesh.
Sources
Related terms
FEA
FEA predicts how a part behaves under loads, heat, or vibration by dividing it into small elements and solving the physics for each one with the finite element method. It is also the engine behind topology optimization and most generative design tools.
Mesh
A mesh represents a shape as a surface of small flat polygons, almost always triangles, joined at shared edges and vertices. Meshes work well for rendering, games, and 3D printing, but they have no true faces, edges, or exact curves, so they are hard to dimension or edit as engineering geometry.
Stress singularity
A stress singularity in finite element analysis is a location where an idealised mathematical model predicts unbounded elastic stress, so the reported peak rises as the mesh is refined instead of converging. Common causes include point loads, point restraints, sharp re-entrant corners, and abrupt idealised boundary conditions.