Abstract
A balanced norm, rather than the common energy norm, is introduced to reflect the behavior of layers more accurately in the finite element method for singularly perturbed reaction–diffusion problems. Convergence of optimal order in the balanced norm has been proved in the case of rectangular finite elements. However, for triangular finite elements Pk (k≥2), it is still open to prove this convergence result. With the help of the L2-stability of a weighted L2 projection, instead of the L∞-stability widely used in existing references, the geometric constraints on meshes are relaxed. As a result, the optimal order convergence in the balanced norm is proved in the case of Bakhvalov–Shishkin triangular meshes. Numerical experiments support theoretical results.
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