The Discontinuous Petrov–Galerkin (DPG) method is a widely employed discretization for Partial Differential Equations (PDEs). In recent work, we applied the DPG with optimal test functions time integration of transient parabolic PDEs. We showed that resulting DPG-based time-marching scheme equivalent to exponential integrators trace variables. this extend aforementioned time-dependent hyperboli...

This paper presents a new multiscale finite element method for the incompressible Navier–Stokes equations. The proposed method arises from a decomposition of the velocity field into coarse/resolved scales and fine/unresolved scales. Modeling of the unresolved scales corrects the lack of stability of the standard Galerkin formulation and yields a method that possesses superior properties like th...