Online Course: Understand the fundamentals of CFD – From FEM to FVM to FDM, by building solvers in MATLAB

Why should you start with FEM in this course?

Finite Element Method (FEM) is the Mathematical Backbone of Computational Fluid Dynamics.
You’ll understand why commercial CFD tools dominate the industry and how their “black-box” nature hides the numerical foundations powering them. FEM isn’t just a discretization technique—it’s a unifying mathematical framework.
By teaching you FEM first, this course helps you build rigorous intuition: FEM’s weak formulations, basis functions, and matrix assembly will reveal to you how numerical methods approximate physics.
Generalizes to FVM / FDM: FEM’s structure allows deriving Finite Volume (FVM) and Finite Difference (FDM) methods, showing their strengths/limitations.
Prepares you for Advanced Research: FEM’s flexibility underpins cutting-edge techniques for future courses (discontinuous Galerkin, multiphysics).

You’ll build a FEM Solver in MATLAB.
Start by building a solver for the driven cavity problem (classic benchmark).
Learn how to program matrix assembly, handle boundary conditions, and solve linear systems.
Derive FVM/FDM from FEM Principles
See how changing test functions or quadrature rules transition you to FVM/FDM.
Decode Commercial Solvers
Map course concepts to tools like OpenFoam / FreeFEM / FEAtool: Understand why sparse solvers dominate. How do preconditioners accelerate convergence?
Explore iterative vs. direct methods, time-stepping trade-offs, and stability analysis.

Mathbridge Takes You From Code to Computational Fluency
Most CFD courses teach tools; this one teaches you thinking. By building FEM, FVM, and FDM solvers, side-by-side, you’ll:
- Learn to Spot Solver Shortcomings: Why does a commercial FVM tool struggle with fluid-structure interaction? How would FEM adapt?
- Debug Like a Pro: Diagnose convergence issues, ill-conditioned matrix, or time-step instability from first principles.
- Own Your Knowledge: Transition seamlessly to advanced topics (fluid-structure interaction, phase-field modeling) in future courses.
Mastering Computational Fluid Dynamic Starts with the Foundations.
Commercial tools solve yesterday’s problems. To tackle tomorrow’s—biomedical flows, smart materials, microfluidics—you need foundational mastery. This course by Mathbridge equips you to see inside the black box, adapt to new methods, and innovate where others hit limits.

Through Mathbridge, start building your FEM solver today, upskill yourself and secure your career in computational fluid dynamics.

Email us at director@mathbridge.in or visit mathbridge.in for more details.

Connect with Mathbridge’s service unit for custom CFD solutions at the edge of academia and industry.

Experimental validation of FEA / CFD using hydrodynamics.

*Available as an online & offline course