Rozza G., Ballarin F., Scandurra L., Pichi F. Real Time Reduced Order Computational Mechanics. Parametric PDEs Worked Out Problems

Springer, 2024. — 180 p.Preface
A Short Introduction to Reduced Basis Method
Worked Out Problems for Beginners: Steady Cases
Worked Out Problem 1: Steady Heat Conduction in a Thermal Block
Worked Out Problem 2: A Linear Elasticity Problem on a Square
Worked Out Problem 3: Thermal Transfer Problem in a Parametrized Geometry
Worked Out Problem 4: A Transport Problem for the 2D Graetz Flow
Worked Out Problem 5: Heat Conduction with Gaussian Flux
Advanced Worked Out Problems: Time Dependent and Nonlinear Cases
Worked Out Problem 6: Unsteady Heat Conduction in a Thermal Block
Worked Out Problem 7: A Nonlinear Elliptic Problem
Worked Out Problem 8: A Nonlinear Parabolic FitzHugh–Nagumo Problem
Real-Life Worked Out Problems: Engineering Applications
Worked Out Problem 9: A Thermal Conduction Problem Through an Extended Surface
Worked Out Problem 10: An Idealized Contact Problem in Linear Elasticity with Friction
Worked Out Problem 11: A Linear Elasticity Application on a Beam Bridge
Fluid Dynamics Worked Out Problems
Worked Out Problem 12: Navier-Stokes System for a Backward-Facing Step
Worked Out Problem 13: Bifurcating Coanda Effect in a Channel
Worked Out Problem 14: Unsteady Navier-Stokes Equations for Vortex Shedding Behind a Cylinder
More Advanced Worked Out Problems
Worked Out Problem 15: Stabilized Reduced Method for an Advection Dominated Problem
Worked Out Problem 16: A Parametrized Elliptic Optimal Control Problem
Worked Out Problem 17: Uncertainty Quantification for a Stochastic Thermal Block