A Finite Element Collocation Method for Quasilinear Parabolic Equations
A Finite Element Collocation Method for Quasilinear Parabolic Equations
Let the parabolic problem $c(x,t,u){u_t} = a(x,t,u){u_{xx}} + b(x,t,u,{u_x}),0 < x < 1,0 < t \leqq T,u(x,0) = f(x),u(0,t) = {g_0}(t),u(1,t) = {g_1}(t)$, be solved approximately by the continuous-time collocation process based on having the differential equation satisfied at Gaussian points ${\xi _{i,1}}$ and ${\xi _{i,2}}$ in subintervals $({x_{i - …