By Rolf Rannacher (auth.), Erwin Stein (eds.)
This direction with 6 teachers intends to offer a scientific survey of modern re seek result of famous scientists on error-controlled adaptive finite aspect equipment in good and structural mechanics with emphasis to problem-dependent suggestions for adaptivity, errors research in addition to h- and p-adaptive refinement recommendations together with meshing and remeshing. demanding functions are of equivalent value, together with elastic and elastoplastic deformations of solids, con tact difficulties and thin-walled constructions. a few significant subject matters could be mentioned, particularly: (i) The growing to be value of goal-oriented and native mistakes estimates for quan tities of interest—in comparability with international mistakes estimates—based on twin finite aspect options; (a) the significance of the p-version of the finite aspect process together with parameter-dependent hierarchical approximations of the mathematical version, for instance in boundary layers of elastic plates; (Hi) the alternative of problem-oriented blunders measures in compatible norms, ponder ing residual, averaging and hierarchical blunders estimates together with the potency of the linked adaptive computations; (iv) the significance of implicit neighborhood postprocessing with stronger try areas for you to get constant-free, i. e. absolute-not purely relative-discretizati- mistakes estimates; (v) The coupling of error-controlled adaptive discretizations and the mathemat ical modeling in similar subdomains, akin to boundary layers. the most targets of adaptivity are reliability and potency, mixed with in sight and entry to controls that are autonomous of the utilized discretization equipment. via those efforts, new paradigms in Computational Mechanics could be learned, specifically verifications or even validations of engineering models.
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Additional info for Adaptive Finite Elements in Linear and Nonlinear Solid and Structural Mechanics
1999). Fast and reliable solution of the NavierStokes equations including chemistry. Comput. Visual. Sci 2:107-122. , and Rannacher, R. (1999). Numerical simulation of laminar femes at low Mach number with adaptive fi nite elements. Combust. Theory Modelling 3:503-534. , Johnson, C , and Rannacher R. (1995). Adaptive error control for multigrid finite element methods. Computing 55:21 \-2%%. , and Rannacher, R. (2000). Adaptive fi nite element methods for optimal control of partial differential equations: basic concepts.
Finite element approximation of the acoustic wave equation: error control and mesh adaptation. East-West J. Numer. Math. 7:263-282. , and Rannacher, R. (2003). Adaptive Finite Element Methods for Differential Equations. Lectures in Mathematics, ETH Zurich, Birkhauser, 2003. Becker, R. (1995). An Adaptive Finite Element Method for the Incompressible Navier-Stokes Equations on Time-Dependent Domains. Doctor Thesis, Preprint 95-44 (SFB 359), Universitat Heidelberg. Becker, R. (2000). An optimal-control approach to a posteriori error estimation for fi nite element discretizations of the Navier-Stokes equations.
75) in Qr, W|3Q = 0 on / , on a space-time region Qr = Q. x I, where Q C R'^ 1, and / = [0,7]; the coefficient (2 may vary in space. This model is used to describe diffusive transport of energy or certain species concentrations. The results of this section are taken from Hartmann (1998); see also Bangerth and Rannacher (2003). 75) is by a Galerkin method in space-time. T] into subintervals /„ = (r„_i,r,,] according to 0 = ro < ... < r„ < ...
Adaptive Finite Elements in Linear and Nonlinear Solid and Structural Mechanics by Rolf Rannacher (auth.), Erwin Stein (eds.)