NGSolve User Meeting 2026 - Tutorial
Disclaimer - About this tutorial
This NGSolve tutorial is wrapped in a light adventure narrative — you are an adventurer, and NGSolve is the Beast you learn to tame. That story is only one of several playful, deliberately childlike touches; alongside it you will find optional further-reading pointers, setup explanations and small visual gimmicks.
None of it is in your way. Each optional kind has a little three-stage lever — off · folded · full — and Gimmicks a simple on/off. Set them once below (or any time from the ⚙ View options gear at the bottom-right of every page) and your choice applies to the whole tutorial — every unit, this visit and the next:
How to run — the per-notebook “where does this run?” tables
Story-telling — the adventure framing (like the call to adventure just below)
Quizzes — the end-of-lesson check-yourself questions
Further reading — links into the i-tutorials, iFEM and the User-Meeting material
Gimmicks — the rolling logo and other little animations
Prefer the bare technical content? Slide what you don’t want to off.
🎭 Your call to adventure
You are an adventurer, freshly setting out to earn your spurs. Every great adventurer keeps a companion creature — some ride dragons, some are shadowed by a phoenix, some sail with a kraken. You were entrusted with the Beast. Stories cling to it: they say it is enormously powerful. But raw power is not yet yours to command — first you must tame it and learn its ways. Already, though, you can feel a vast potential slumbering inside it…
This is your training. By the end you will command NGSolve to solve a whole class of problems for you. The steps:
I · Taming the Beast — earn its trust: weak forms, geometry & mesh, first PDEs
II · In the Saddle — ride together: features for real applications
III · Taking Flight — advanced techniques
Afterwards comes The Grand Expedition — the NGSolve User Meeting, where you will see how much more power can be unleashed with NGSolve.
🎭 The three parts
Taming
Riding
Flying
0 · Setting out — install & run¶
Brand new, or installing NGSolve for the first time? Unit 0 is your on-ramp — it covers installation, the different ways to use these notebooks, and the classic ways to run NGSolve. The two quickest ways in are one click away.
JupyterLite runs NGSolve directly in your browser — no installation. Opens the index notebook; every unit is one click away from there.
Run in the cloud on Google Colab. Opens the index notebook, which links on to every unit.
All notebooks (.ipynb + .py) and materials as a ZIP for running locally.
I · Taming the Beast — basics, geometries & first PDEs¶
Earn the Beast’s trust by mastering the core craft — meet it on a first PDE, conjure geometry & mesh, wield functions on the mesh, the finite element spaces, solving with Dirichlet data, and the solver toolbox — until it lets you climb on.
1 · Meet the Beast
The whole NGSolve loop — geometry & mesh, a variational solve, visualization — on your companion creature.
2 · Creating Geometry and Meshes
Forge a sword and a shield, tame the mesh.
3 · What is a CoefficientFunction?
local/world coordinates, regions, ... and a creative way to implement FEM
4 · A zoo of finite element spaces
Explore some of NGSolve finite element spaces.
5 · First linear solve
Solving linear variational problems and how to treat Dirichlet data.
6 · The solver toolbox 🛠
Direct vs iterative solvers, a short glimpse on solvers.
II · In the Saddle — features for applications¶
The second tutorial broadens the toolkit: a mixed (saddle-point) problem, then the three pillars of real simulations — time stepping, discontinuous Galerkin / HDG, and nonlinear solves.
7 · Mixed problems — the saddle point 🐎
Product FESpaces, block systems, scalar constraints
8 · Unsteady problems — the double-glazing flow
Time marching with implicit discretizations.
9 · Discontinuous Galerkin & HDG
Non-conforming methods & upwind stabilization.
10 · Nonlinear problems — Allen–Cahn & Newton
Newton’s method on a phase-separation flow.
III · Taking Flight — advanced techniques¶
The third tutorial takes flight — the genuinely advanced applications, each fusing the building blocks of Parts I & II, closing with the Grand Expedition outlook.
11 · A different pattern: encounter with a relative 🧬
Turing patterns on the curved surface of the beast.
12 · A crowd heads for coffee 🚶☕
Pedestrian flow model: the crowd, the coffee and the jam.
13 · A puffing thermal plume 🔥🌀
A buoyant plume: IMEX with Hdiv/HDG
14 · Melting the chocolate 🍫☕
A phase-field Stefan problem: melting chocolate.
15 · Deforming domains (ngsxfem) 🫧
A two-phase rising bubble on an unfitted mesh (ngsxfem).
The Grand Expedition — an outlook beyond the Beast¶
You have tamed the Beast. The real expedition begins at the NGSolve User Meeting 2026 (event page) and its fantastic contributions — research codes and extensions built on exactly the bricks above. Unit 15 (above) opens that door directly with unfitted / CutFEM methods (ngsxfem); beyond it lie many applications, add-ons, extensions, and deeper insights into the Beast’s power. ☕
