Superconvergence of a Galerkin FEM for Higher-Order Elements in Convection-Diffusion Problems

2013/07/29 by Franz, S., Roos, H. -G.
#65N12 #65N30 #65N50 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1307.7543

Abstract

In this paper we present a first supercloseness analysis for higher-order Galerkin FEM applied to a singularly perturbed convection-diffusion problem. Using a solution decomposition and a special representation of our finite element space we are able to prove a supercloseness property of order p+1/4 in the energy norm where the polynomial order p>=3 is odd.

Related

• Supercloseness of finite element method for a singularly perturbed convection-diffusion problem on Bakhvalov-type mesh in 2D
• Superconvergence analysis of FEM and SDFEM on graded meshes for a problem with characteristic layers
• Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem
• Supercloseness of the NIPG method for a singularly perturbed convection diffusion problem on Shishkin mesh
• Supercloseness of the DDG method for a singularly perturbed convection diffusion problem on Shishkin mesh