On the performance of high-order finite elements with respect to maximum principles and the non-negative constraint for diffusion-type equations

Details On the performance of high-order finite elements with respect to maximum principles and the non-negative constraint for diffusion-type equations On the performance of high-order finite elements with respect to maximum principles and the non-negative constraint for diffusion-type equations

2011-08-03

arxiv.org/abs/1108.0952v1

Computer Science

Numerical Analysis

Scientific paper

The main aim of this paper is to document the performance of $p$-refinement with respect to maximum principles and the non-negative constraint. The model problem is (steady-state) anisotropic diffusion with decay (which is a second-order elliptic partial differential equation). We considered the standard single-field formulation (which is based on the Galerkin formalism) and two least-squares-based mixed formulations. We have employed non-uniform Lagrange polynomials for altering the polynomial order in each element, and we have used $p = 1, ..., 10$. It will be shown that the violation of the non-negative constraint will not vanish with $p$-refinement for anisotropic diffusion. We shall illustrate the performance of $p$-refinement using several representative problems. The intended outcome of the paper is twofold. Firstly, this study will caution the users of high-order approximations about its performance with respect to maximum principles and the non-negative constraint. Secondly, this study will help researchers to develop new methodologies for enforcing maximum principles and the non-negative constraint under high-order approximations.

Affiliated with

Also associated with

No associations

Rating

On the performance of high-order finite elements with respect to maximum principles and the non-negative constraint for diffusion-type equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the performance of high-order finite elements with respect to maximum principles and the non-negative constraint for diffusion-type equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the performance of high-order finite elements with respect to maximum principles and the non-negative constraint for diffusion-type equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-13567