Mesh Independence Analysis

Mesh independence analysis, also called a mesh convergence study, determines whether an FEA result has become sufficiently insensitive to further mesh refinement. The usual procedure is to solve the same model with progressively smaller elements while keeping geometry, material properties, loads, and boundary conditions unchanged, then compare selected quantities of interest. A relative change between two meshes can be calculated as ΔR = |R_fine - R_coarse| / |R_fine| × 100%, where R is the selected result. The acceptable change is problem-dependent; 5% is a commonly used engineering criterion, not a universal requirement. Displacement and reaction quantities often converge more readily than local stresses. A particularly important exception is a stress singularity caused by idealizations such as a sharp re-entrant corner, point load, or perfectly rigid constraint. At an ideal singularity, the calculated peak stress can continue increasing as the mesh is refined, so the maximum nodal or elemental stress at that location is not a suitable convergence metric. The singular geometry may need to be represented with a realistic fillet, or stress should be evaluated at a defined distance away from the singularity. h-convergence reduces the characteristic element size h, while p-convergence increases the polynomial order p of the element interpolation functions. A useful convergence study compares the same physical quantity against element size, element count, or degrees of freedom and checks whether successive refinements approach a stable value. Mesh refinement alone does not correct poor element quality, inappropriate boundary conditions, or an incorrect physical model.