Journal of Computational Physics
Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
Mathematics and Computers in Simulation
Anisotropic error control for environmental applications
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations
Journal of Computational Physics
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Original Articles: 3D Metric-based anisotropic mesh adaptation for vortex capture
Mathematics and Computers in Simulation
Continuous Mesh Framework Part I: Well-Posed Continuous Interpolation Error
SIAM Journal on Numerical Analysis
Continuous Mesh Framework Part II: Validations and Applications
SIAM Journal on Numerical Analysis
A Numerical Study of Some Hessian Recovery Techniques on Isotropic and Anisotropic Meshes
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
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The anisotropic error indicator presented in [M. Picasso, Comm. Numer. Methods Engrg., 19 (2003), pp. 13--23.] in the frame of the Laplace equation is extended to elliptic and parabolic problems. Our error indicator is derived using the anisotropic interpolation estimates of [L. Formaggia and S. Perotto, Numer. Math., 89 (2001), pp. 641--667; L. Formaggia and S. Perotto, Numer. Math., (2002), DOI 10.1007/s002110200415], together with a Zienkiewicz--Zhu error estimator to approach the error gradient. A numerical study of the effectivity index is proposed for elliptic, diffusion-convection, and parabolic problems. An adaptive algorithm is implemented, aimed at controlling the relative estimated error.