Mesh dependent stability and condition number estimates for finite element approximations of parabolic problems (Q2862518)

The paper analyzes the effects of spatial simplicial meshes on the stability and the conditioning of fully discrete approximations of a parabolic equation using a general finite element discretization in space with explicit or implicit marching in time. The authors derive a new time step size condition for the explicit time integration schemes presented, which provides more precise dependence not only on mesh size but also on mesh shape. The paper also establishes some explicit mesh dependent estimates of the spectral condition number of the resulting linear systems, for implicit time integration schemes.