DOLFIN User Manual - FEniCS Project
DOLFIN User Manual - FEniCS Project
DOLFIN User Manual - FEniCS Project
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<strong>DOLFIN</strong> <strong>User</strong> <strong>Manual</strong>Hoffman, Jansson, Logg, Wellsu = x − X,˙u − v = 0 in Ω 0 ,˙v − ∇ · σ = f in Ω 0 ,σ = Eɛ(u) = E(∇u ⊤ + ∇u)Eɛ = λtr(ɛ)I + 2µɛ,v(0, ·) = v 0 , u(0, ·) = u 0 in Ω 0 ,u = g D on Γ 1 × (0, T ],−∂ n u = 0 on Γ 2 × (0, T ]The variational form:∫−σ(u)ɛ(v) + fw dx,Ω Ω∀w. (12.4)The time integration is done using dG(0) (backward Euler).The mass matrix appearing from ∫ Ωit using nodal quadrature).˙vwdx is lumped (equivalent to computing12.4.1 UsagePresent API of solver and give an example.12.4.2 PerformanceWrite something about the performance of the solver.12.4.3 LimitationsWrite something about the limitations of the solver.83
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