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FDM vs FEM vs FVM
FDM, FEM, and FVM are three foundational numerical methods used across mechanical, civil, and aerospace engineering from heat transfer analysis to CFD to structural simulation.
The difference between them confuses students because textbooks explain them separately.
This interactive simulation solves the same 2D heat conduction problem using all three methods side by side same boundary conditions, same grid, same physics so you can see exactly how each method discretizes the domain differently.
FDM uses node-based finite differences on a structured grid. FEM divides the domain into triangular elements with shape functions.
FVM builds control volumes and tracks flux conservation. Switch between them in one tap, adjust grid size and heat source, and watch the solution converge step by step.
Built for GATE preparation, university coursework, and engineers choosing between ANSYS, Fluent, and custom solvers.
Try this simulation yourself
Start on the FDM tab — you'll see a structured grid with temperature values at each node. Hit Solve and watch heat diffuse from the hot top edge downward, one Jacobi iteration at a time. Notice the 5-point stencil highlighted at the center — T equals the average of its 4 neighbors. That's the entire FDM idea.
Switch to FEM — same nodes, but now connected into triangles. Each triangle fills with a color based on the average temperature of its 3 corner nodes. The highlighted element shows the shape function equation N₁T₁ + N₂T₂ + N₃T₃ — FEM interpolates inside the element, not just at grid points. Hit Solve and watch the triangles color in as heat spreads.
Switch to FVM — now you see rectangular control volumes around each node. Small arrows appear between cells showing heat flux direction — always from hot to cold. The highlighted cell shows the rule: total flux in equals total flux out. This is why FVM is called "inherently conservative" — it enforces energy balance at every cell, every step.
Increase the grid size from 5 to 12 — all three methods get more accurate. More nodes, more elements, more volumes. This is mesh refinement — the most important concept in any simulation.
Crank the heat source up to 500°C — watch the color gradient stretch. The temperature legend at the bottom shows the full range from blue (cold) to red (hot).
Use Step +1 instead of Solve — click it slowly. Watch how each iteration brings the solution closer to steady state. Early steps show big changes. Later steps barely move — that's convergence.