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The elliptic problem-div⁡(μ⁢∇⁡u)=f-\operatorname{div}(\mu\nabla u)=fis considered, whereμ&gt;0\mu&gt;0is smooth but strongly varying. Anisotropic a posteriori error estimates are derived, the effectivity index being bounded above and below by two constants independent of the data , , the mesh size and aspect ratio, up to higher order terms. Numerical experiments on non-adapted and adapted anisotropic meshes confirm these predictions.

Anisotropic Adaptive Finite Elements for an Elliptic Problem with Strongly Varying Diffusion Coefficient