A coarse mesh smooths right over sharp stress concentrations, giving a lower, misleadingly comfortable answer. Refine the mesh and watch the approximation climb toward the true peak stress it was missing.
Finite element analysis (FEA) approximates the behavior of a complex structure by dividing it into a mesh of small, simple-shaped elements, solving the governing equations on each element, and assembling the results into an approximate solution across the whole domain. Because it's fundamentally an approximation — not an exact closed-form solution — how finely that mesh is divided directly affects how accurate the result actually is.
Exact closed-form solutions exist for only a small number of simple geometries and loading conditions. FEA instead approximates the true, continuously varying stress or displacement field using a finite number of discrete elements, each assumed to follow a simplified (typically polynomial) behavior internally — the true field is only approximated at element boundaries and interpolated within them, which is inherently different from an exact analytical solution.
A coarse mesh, with few large elements, can only crudely approximate rapidly changing fields — sharp stress concentrations near corners, holes, or load points get smoothed over and understated, exactly as shown in the visualization above. Refining the mesh (more, smaller elements) lets the approximation follow the true field's actual shape more closely, generally converging toward the true solution as element size approaches zero — this is why 'mesh convergence' is a standard, expected part of any serious FEA workflow.
Refining a mesh indefinitely isn't free — it dramatically increases computation time and resource requirements. Real FEA practice runs a mesh convergence study: solving the same problem at progressively finer mesh densities and confirming the result stops changing meaningfully between refinements, which gives confidence the solution has actually converged to the true answer rather than merely being 'finer than the last attempt' without verified accuracy.
A coarse mesh, made of larger elements with typically simple (often linear) internal behavior, physically cannot represent a sharp localized stress spike well — it effectively smooths and averages that spike out over the larger element, understating the true local peak. This is why stress concentrations (holes, fillets, sharp corners) specifically require mesh refinement in those local regions to capture accurately.
In general, yes, up to a point — but numerical issues (rounding error accumulation, poorly shaped elements, or fundamental modeling errors like incorrect boundary conditions or material properties) mean a finer mesh alone cannot fix a fundamentally flawed model. Mesh refinement improves the numerical approximation of a correctly set up model; it cannot correct an incorrect one.
Because computational cost (solve time, memory) grows rapidly with element count, and past the point of convergence, further refinement gives no meaningful accuracy improvement for significant added cost — the whole purpose of a mesh convergence study is to find the coarsest mesh that still gives an accurate result, balancing accuracy against practical computational budget.
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