Standard syllabus
Finite element methods · Graduate · Engineering
Topics
Weak form and element formulations
- Calculus of variations and Euler-Lagrange equations
- Weighted residual methods: Galerkin approach
- Weak form derivation for Poisson and elasticity problems
- Shape functions for 1D and 2D elements
- Isoparametric mapping and numerical integration
- Element stiffness and mass matrix assembly
- Patch test and element completeness
- Locking phenomena: shear and volumetric
- Mixed formulations and reduced integration
- A priori and a posteriori error estimates (intro)
Solvers and nonlinear extensions
- Direct versus iterative linear solvers
- Preconditioning and sparse matrix storage
- Newton-Raphson for nonlinear equilibrium
- Material nonlinearities: plasticity intro
- Contact algorithms: penalty and Lagrange multipliers
- Large deformation and updated Lagrangian formulations
- Dynamic FE: Newmark time integration
- Eigenvalue solvers for modal analysis
- Adaptive mesh refinement strategies
- Parallel FE on HPC clusters
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.