Adaptive Galerkin finite element methods for partial differential equations

By Rolf Rannacher. 2001

102 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/045c43776939d2b532f5d8f71c35fd2c70c99248

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In Computational Mechanics

In Mechanics of Materials

In Statistical and Nonlinear Physics

Citations in the corpus

Adjoint and defect error bounding and correction for functional estimates (2003, methodology): “The issues of error bounding and adaptive error control have received particular attention in the finite element community [2,15–28], where the use of the adjoint PDE for error analysis was first investigated.”
A low order Galerkin finite element method for the Navier–Stokes equations of steady incompressible flow: a stabilization issue and iterative methods (2002, methodology): “2002 Published by Elsevier Science B.V. Keywords: Navier–Stokes equations; Finite elements; Stabilized method; Oseen problem; Iterative methods”
Numerical Solution of Richards' Equation: A Review of Advances and Challenges (2017, background): “However, despite the introduction of sophisticated adaption techniques that have have matured in other computational mechanics fields (Schwab, 1998; Rannacher, 2001; Fidkowski and Darmofal, 2011), including so-called h adaption which modifies the local mesh spacing (Pettway et al., 2010) as well as…”
Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics (2011, methodology): “using a higher-accuracy stencil [37] [40] [66] [67].”
Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows (2003, background): “Becker, Rannacher and collaborators [8,9,11,42] have developed an optimal control approach for output-based grid adaptation within a Galerkin finite element framework.”
Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations (2014, methodology): “In contrast, most implementations of the dualweighted residual method require an approximation to the adjoint on a refined space [95, 96, 97, 98, 99].”
Numerical study of the effectivity index for an anisotropic error indicator based on Zienkiewicz–Zhu error estimator (2002, methodology): “The framework of [ 9 ] was considered and anisotropic estimators for functionals of the error were derived.”