FEniCS Course - FEniCS Project

More documents

Recommendations

Info

Hello World!We will solve Poisson’s equation, the Hello World of scientificcomputing:−∆u = fu = u 0in Ωon ∂ΩPoisson’s equation arises in numerous contexts:• heat conduction, electrostatics, diffusion of substances,twisting of elastic rods, inviscid fluid flow, water waves,magnetostatics• as part of numerical splitting strategies of morecomplicated systems of PDEs, in particular theNavier–Stokes equations2 / 22
The FEM cookbookAu = f(i)Partial differential equationMultiply by vTake V h ⊂ VLet u h = ∑ j U jφ j(ii)a(u, v) = L(v) Continuous variational problem(iii)a(u h , v) = L(v) Discrete variational problem(iv)AU = b System of discrete equations3 / 22
Page 1: FEniCS CourseLecture 2: Static line
Page 5 and 6: Deriving a variational problem for
Page 7 and 8: Discrete variational problem for Po
Page 9 and 10: A test problemWe construct a test p
Page 11 and 12: Step by step: the first lineThe fir
Page 13 and 14: Step by step: creating a function s
Page 15 and 16: Step by step: defining a boundary c
Page 17 and 18: Step by step: defining the right-ha
Page 19 and 20: Step by step: solving variational p
Page 21 and 22: Python/FEniCS programming 1011 Open

FEniCS Course - FEniCS Project

Create successful ePaper yourself

Delete template?

Save as template?