1load "Element_Mixte" 2/* 3 Solving the following Poisson problem 4 Find $p$, such that; 5 $ - \Delta p = f $ on $\Omega$, 6 $ dp / dn = (g1d,g2d). n $ on $\Gamma_{123}$ 7 $ p = gd $ on $\Gamma_{1}$ 8 with de Mixte finite element formulation 9 Find $p\in L^2(\Omega) and $u\in H(div) $ such than 10 u - Grad p = 0 11 - div u = f 12 $ u. n = (g1d,g2d). n $ on $\Gamma_{123}$ 13 $ p = gd $ on $\Gamma_{1}$ 14 15 the variationnel form is: 16 $\forall v\in H(div)$; $v.n = 0$ on $\Gamma_{4}\} $: $ \int_\Omega u v + p div v -\int_{\Gamma_{123}} gd* v.n = 0 $ 17 18 $\forall q\in L^2$: $ -\int_\Omega q div u = \int_Omega f q $ 19and $ u.n = (g1n,g2n).n$ on $\Gamma_4$ 20 21*/ 22mesh Th=square(10,10); 23fespace Vh(Th,RT1); 24fespace Ph(Th,P1dc); 25 26func gd = 1.; 27func g1n = 1.; 28func g2n = 1.; 29func f = 1.; 30 31Vh [u1,u2],[v1,v2]; 32Ph p,q; 33 34problem laplaceMixte([u1,u2,p],[v1,v2,q],solver="SPARSESOLVER",eps=1.0e-10,tgv=1e30,dimKrylov=150) = 35 int2d(Th)( p*q*0e-10+ u1*v1 + u2*v2 + p*(dx(v1)+dy(v2)) + (dx(u1)+dy(u2))*q ) 36 + int2d(Th) ( f*q) 37 - int1d(Th,1,2,3)( gd*(v1*N.x +v2*N.y)) // int on gamma 38 + on(4,u1=g1n,u2=g2n); 39 40 laplaceMixte; 41 plot([u1,u2],coef=0.1,wait=1,ps="o/lapRTuv.eps",value=true); 42 plot(p,fill=1,wait=1,ps="o/laRTp.eps",value=true); 43