Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and $L^1$ contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in $L^1$ and $L^{\infty }$, respectively, of the scheme are established. Under certain hypotheses on the data, we also derive $L^1$ convergence without any convergence rate....

Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and L1 contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in L1 and L∞, respectively, of the scheme are established. Under certain hypotheses on the data, we also derive L1 convergence without any...

We prove the following theorem: Let p > 1 and let E be a real p-uniformly convex Banach space, and C a nonempty bounded closed convex subset of E. If $T=T_s:C\to C:s\in G=[0,\infty )$ is a Lipschitzian semigroup such that $g=limin{f}_{G\ni \alpha \to \infty }in{f}_{G\ni \delta \ge 0}1/\alpha {ʃ}_0^{\alpha }\parallel T_{\beta +\delta }{\parallel }^{p}d\beta <1+c$, where c > 0 is some constant, then there exists x ∈ C such that $T_{s}x=x$ for all s ∈ G.