FEniCS Course - FEniCS Project
FEniCS Course - FEniCS Project FEniCS Course - FEniCS Project
The FEniCS challenge!Solve the partial differential equation−∆u = fwith homogeneous Dirichlet boundary conditions on the unitsquare for f(x, y) = 2π 2 sin(πx) sin(πy). Plot the error in the L 2norm as function of the mesh size h for a sequence of refinedmeshes. Try to determine the convergence rate.• Who can obtain the smallest error?• Who can compute a solution with an error smaller thanɛ = 10 −6 in the fastest time?The best students(s) will be rewarded with an exclusive FEniCSsurprise!Hint: help(errornorm)22 / 22
- Page 1 and 2: FEniCS CourseLecture 2: Static line
- Page 3 and 4: The FEM cookbookAu = f(i)Partial di
- 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: Python/FEniCS programming 1011 Open
The <strong>FEniCS</strong> challenge!Solve the partial differential equation−∆u = fwith homogeneous Dirichlet boundary conditions on the unitsquare for f(x, y) = 2π 2 sin(πx) sin(πy). Plot the error in the L 2norm as function of the mesh size h for a sequence of refinedmeshes. Try to determine the convergence rate.• Who can obtain the smallest error?• Who can compute a solution with an error smaller thanɛ = 10 −6 in the fastest time?The best students(s) will be rewarded with an exclusive <strong>FEniCS</strong>surprise!Hint: help(errornorm)22 / 22
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