16 research outputs found
Boundary Regularity for Nonlinear Elliptic Systems: Applications to the Transmission Problem
No full textEbmeyer C, Frehse J, Kaßmann M. Boundary regularity for nonlinear elliptic systems: applications to the transmission problem. In: Geometric analysis and nonlinear partial differential equations. Springer, Berlin; 2003: 505-517
Optimal convergence for the implicit space-time discretization of parabolic systems with -structure
No full textDiening L, Ebmeyer C, Růžička M. Optimal convergence for the implicit space-time discretization of parabolic systems with -structure. SIAM Journal on Numerical Analysis. 2007;45(2):457-472
Regularity in Sobolev spaces for the fast diffusion and the porous medium equation
No full textAbstractThe degenerate parabolic equation ut=Δ(|u|m−1u),m>0 is considered in a cylinder Ω×(0,T) under homogeneous Dirichlet boundary values. The regularity of weak solutions for the fast diffusion equation (m<1) and the porous medium equation (m>1) are investigated. Regularity of u and |u|m−1u in weighted Sobolev spaces and in fractional order Nikolskii spaces are proved
Global Regularity in Sobolev Spaces for Elliptic Problems with p-structure on Bounded Domains
No full textQuasi-Norm interpolation error estimates for the piecewise linear finite element approximation of p-Laplacian problems
No full textIn this work, new interpolation error estimates have been derived for some well-known interpolators in the quasi-norms. The estimates are found to be essential to obtain the optimal a priori error bounds under the weakened regularity conditions for the piecewise linear finite element approximation of a class of degenerate equations. In particular, by using these estimates, we can close the existing gap between the regularity required for deriving the optimal error bounds and the regularity achievable for the smooth data for the 2-d and 3-d p-Laplacian
Finite Element Approximation of the Fast Diffusion and the Porous Medium Equations
No full textThe fast diffusion equation u(t) =Delta(vertical bar u vertical bar(m- 1)u)(0 < m < 1) and the porous medium equation (1 < m < infinity) are studied in a parabolic cylinder Omega x (0, T). A fully discrete Galerkin approximation is considered using C-0-piecewise linear finite elements in space and the backward Euler time discretization. A priori error estimates in quasi norms and rates of convergence are proved
Quasi-steady Stokes flow of multiphase fluids with shear-dependent viscosity
No full textThe quasi–steady power–law Stokes flow of a mixture of incompressible fluids
with shear–dependent viscosity is studied. The fluids are immiscible and have constant
densities. Existence results are presented for both the no–slip and the no–stick boundary
value conditions. Use is made of Schauder’s fixed–point theorem, compactness arguments,
and DiPerna-Lions renormalized solutions.CMUC/FCT; Project POCI/MAT/57546/200
