Alexios Zervos

Alexios Zervos spent his working life on a question most practitioners skip: not "what does the simulation say," but "how do you know it is right." For forty years his subject was the finite-element method and its verification — the a-priori error estimates that promise a convergence rate, and the manufactured solutions that confirm the code actually achieves it. He wrote solvers for linear elasticity, steady and transient heat, and the coupled thermo-mechanical problems where the two meet, and for each one he wrote the exact solution that proved the solver converged at the order the theory demanded. A code that recovered a known answer at the predicted rate was a code he trusted; a code that merely produced a plausible picture was, to him, an untested claim.

He is, by temperament, a verifier. The habit was forced on him early by a stress calculation that looked entirely reasonable and was entirely wrong — the elements had locked, and nothing on the screen said so. It never left him. When DOLFINx arrived and the finite-element community began migrating off the legacy FEniCS stack onto a faster, cleaner, still-stabilizing library, he saw both the opportunity and the danger: a new tool is exactly when old verification habits lapse.

This book is his answer. It solves partial differential equations with DOLFINx and the FEniCSx stack, and it verifies every method the same way he always has — by the method of manufactured solutions, by confirmed convergence orders, by analytic matches on the simple shapes that have them, and by physical conservation on the irregular parts that do not. He is now retired from teaching and writes on computational mechanics.