On the performance of high-order finite elements with respect to maximum principles and the nonnegative constraint for diffusion-type equations Academic Article uri icon

abstract

  • SUMMARYThe main aim of this paper is to document the performance of prefinement with respect to maximum principles and the nonnegative constraint. The model problem is steadystate anisotropic diffusion with decay (which is a secondorder elliptic partial differential equation). We consider the standard singlefield formulation based on the Galerkin formalism and two least squaresbased mixed formulations. We employ Lagrange polynomials with unequalspaced points, and polynomials of order p=1 to p=10 are used. It is shown that the violation of the nonnegative constraint cannot be overcome with prefinement alone for anisotropic diffusion. We shall illustrate the performance of prefinement by using several representative problems. The intended outcomes of the paper are twofold. First, this study will caution the users of highorder approximations about their performance with respect to maximum principles and the nonnegative constraint. Second, this study will help researchers develop new methodologies for enforcing maximum principles and the nonnegative constraint under highorder approximations. Copyright 2012 John Wiley & Sons, Ltd.

published proceedings

  • INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

author list (cited authors)

  • Payette, G. S., Nakshatrala, K. B., & Reddy, J. N.

citation count

  • 9

complete list of authors

  • Payette, GS||Nakshatrala, KB||Reddy, JN

publication date

  • August 2012

publisher