Bubble and multiscale stabilization of bilinear finite element methods for transient advection-diffusion equations on rectangular grids

Stability of the Residual Free Bubble Method for Bilinear Finite Elements on Rectangular Grids

Multiscale finite elements through advection-induced coordinates for transient advection-diffusion equations

Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable long term simulations. This is typically done via parametrizations but their coupling to the coarse grid variables often involves simple heuristics. We explo...

A lowest order divergence-free finite element on rectangular grids

It is shown that the conforming Q2,1;1,2-Q ′ 1 mixed element is stable, and provides optimal order of approximation for the Stokes equations on rectangular grids. Here Q2,1;1,2 = Q2,1 ×Q1,2 and Q2,1 denotes the space of continuous piecewise-polynomials of degree 2 or less in the x direction but of degree 1 in the y direction. Q′1 is the space of discontinuous bilinear polynomials, with spurious...

Positivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations

Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...

A parameter-free stabilized finite element method for scalar advection-diffusion problems

We formulate and study numerically a new, parameter-free stabilized finite element method for advectiondiffusion problems. Using properties of compatible finite element spaces we establish connection between nodal diffusive fluxes and one-dimensional diffusion equations on the edges of the mesh. To define the stabilized method we extend this relationship to the advection-diffusion case by solvi...