Abstract ▼ AI-Helper

A stabilized hp‐finite element method (FEM) of Galerkin least squares (GLS) type is analysed for the Stokes equations in polygonal domains. Contrary to the standard Galerkin FEM, the GLSFEM admits the implementationally attractive equal‐order interpolation in the velocity and the press...

A stabilized hp‐finite element method (FEM) of Galerkin least squares (GLS) type is analysed for the Stokes equations in polygonal domains. Contrary to the standard Galerkin FEM, the GLSFEM admits the implementationally attractive equal‐order interpolation in the velocity and the pressure. In conjunction with geometrically refined meshes and linearly increasing approximation orders it is shown that the hp‐GLSFEM leads to exponential rates of convergence for solutions exhibiting singularities near corners. To obtain this result a novel hp‐interpolation result is proved that allows the approximation of pressure functions in certain weighted Sobolev spaces in a conforming way and at exponential rates of convergence on geometric meshes.