Robust Globally Divergence-Free Weak Galerkin Finite Element Methods for Natural Convection Problems

Robust Globally Divergence-free Weak Galerkin Methods for Stokes Equations

This paper proposes and analyzes a class of robust globally divergence-free weak Galerkin (WG) finite element methods for Stokes equations. The new methods use the Pk/Pk−1 (k ≥ 1) discontinuous finite element combination for velocity and pressure in the interior of elements, and piecewise Pl/Pk (l = k − 1, k) for the trace approximations of the velocity and pressure on the inter-element boundar...

Parallel Adaptive Finite Element Methods for Problems in Natural Convection

Finite Element Methods for Convection Diffusion Equation

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

Taylor-Galerkin-based spectral element methods for convection-diffusion problems

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A Posteriori Error Estimates for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems

A residual type a posteriori error estimator is presented and analyzed for Weak Galerkin finite element methods for second order elliptic problems. The error estimator is proved to be efficient and reliable through two estimates, one from below and the other from above, in terms of an H1-equivalent norm for the exact error. Two numerical experiments are conducted to demonstrate the effectivenes...