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Abstract
we present a first supercloseness analysis for higher order FEM/LDG coupled method for solving singularly perturbed convection-diffusion problem. Based on piecewise polynomial approximations of degreek (k≥1), a supercloseness property ofk+1/2in DG norm is established on S-type mesh. Numerical experiments complement the theoretical results.
Highlights
2. The S-Type Mesh and the FEM/local discontinuous Galerkin (LDG) Coupled Method
In this paper we are interested in the construction and validation of high-order finite element approximations to problems of type−εu − bu + cu = f in Ω = (0, 1), (1)u (0) = u (1) = 0, where 0 < ε ≪ 1 is a small positive parameter and b, c, and f are sufficiently smooth functions with the following properties:b (x) ≥ β > 0, c (x) ≥ 0, c (x) + 1 2 b ≥ c0 > ∀x ∈ Ω, (2)for some constants β and c0
Some properties of S-type mesh are given in the following lemma
Summary
2. The S-Type Mesh and the FEM/LDG Coupled Method Given an arbitrary function φ fulfilling these conditions, a S-type mesh is defined. Some properties of S-type mesh are given in the following lemma.
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