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3 cards from this section. Quick, good the night before a test.
What does FDM stand for?
Remember the focus on how we approximate derivatives.
What is the main advantage of using FEM?
Think about problems with uneven shapes.
What do PDEs model?
Consider the context of heat and fluid dynamics.
True or False: FDM is effective for complex geometries.
Remember the limitations discussed on geometries.
Solve the following heat equation using FDM: ∂u/∂t = α∂²u/∂x² with u(0,t)=0, u(L,t)=0, and initial condition u(x,0)=f(x). Outline your approach carefully.
Think about how the boundary conditions affect your grid.
Using FEM, reformulate the Poisson equation -d²u/dx² = f(x) into its weak form, and describe the steps to set up the global system of equations.
Remember integration by parts reduces derivatives in the equation.
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