A numerical procedure for the porous media equation (Q1086095)

The paper is concerned with an attempt to derive a procedure for obtaining the numerical solution of the porous medium problem \(u_ t=(u^ 2)_{xx}\), \(u(0,x)=u_ 0(x)\), \(u_ 0(x)\geq 0\), \(t>0\), \(x\in R\). The problem appears to be parabolic but it has some distinctly hyperbolic features. The boundary is also a moving one. The approach uses a variational formulation. The idea of finite elements is used. Numerical results are presented for a particular situation. Stability is obtained. The paper will be interesting to numerical analysis.