LiberalArts
October 19, 2019
420

# Partial differential equation_1 Finite element method

https://note.mu/lib_arts/n/n45f1fc24bafb

October 19, 2019

## Transcript

2. ### / 2 . 1 Copyright © Liberal Arts Community. All

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3. ### / 2 ( ) (Poisson ) ( ) ( )

= α∇ u ∂t ∂u 2 −∇ u = f(r) 2 = ∇ u c2 1 ∂t2 ∂ u 2 2 ∇ = 2 + ∂x2 ∂2 ∂y2 ∂2 2 . 2 Copyright © Liberal Arts Community. All Rights Reserved.

7. ### / 3 . 1 Copyright © Liberal Arts Community. All

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13. ### / 1. 2. 1 P1 1 , P2 2 3.

: int n = 100; border C(t=0,1){x=cos(2*pi*t); y=sin(2*pi*t);}; mesh Th = buildmesh(C(n)); fespace Vh(Th,P1); ∇u ⋅ ∫ Ω ∇v dV = fv dV ∫ Ω Vh u,v; problem Poisson(u,v) = int2d(Th)( dx(u)*dx(v)+dy(u)*dy(v) ) - int2d(Th)( f*v ); Poisson; 3 . 7 Copyright © Liberal Arts Community. All Rights Reserved.

16. ### / 4 . 3 Copyright © Liberal Arts Community. All

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17. ### / : ( ): : = α∇ u ∂t ∂u

2 ∼ ∂t ∂u Δt u −u i i−1 v dV + α∇u ⋅ ∇v dV = 0 ∫ Ω ( Δt u − u i i−1 ) ∫ Ω i 4 . 4 Copyright © Liberal Arts Community. All Rights Reserved.