FEM & CFD, Poisson & Convection–Diffusion, SUPG Stabilization, Variational Principles & Error Analysis
What you will learn
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Solve practical 1D scenarios: Heat transfer with source, Reaction with Diffusion through highly accessible excel sheets
Develop intuition on solving the practical problem of mixing/heat transfer along with flow. Tackle the difficulties through ‘upwinding/SUPG’
Write differential equations using conservation laws which represent the reality, avoiding ill posed unsolvable equations
Learn both the Practical Conservation and abstract Variational approach for solving PDEs which are foundational to real industrial problems
Juggle between finite differences/volumes/elements on the same problem and observe their practical nuances
Quickly observe the complete real time dynamic matrix data structure for finite elements/differences/volumes
Understand error analysis & convergence plots: L₂ error norms and generation of log–log plots to assess solution accuracy and convergence rates.
Extra content: 1D Julia code—Poisson & SUPG solver reads Gmsh meshes, runs grid-convergence study using manufactured solutions for various polynomial orders.
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