Convergence of local projection stabilisation finite element methods for convection–diffusion problems on layer-adapted meshes

Abstract

We present a minor modification of of the stabilisation term in the local projection stabilisation (LPS) method for stabilising singularly perturbed problems on layer-adapted meshes, such that the error can be estimated uniformly and in optimal order in the associated LPS-norm, which is stronger than the standard energy norm. Numerical results confirm the theoretical findings.