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Van der Zee, K.G. (author), Van Brummelen, E.H. (author), De Borst, R. (author)We develop duality-based a posteriori error estimates for functional outputs of solutions of free-boundary problems via shape-linearization principles. To derive an appropriate dual (linearized adjoint) problem, we linearize the domain dependence of the very weak form and goal functional of interest using techniques from shape calculus. We show...journal article 2010
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Van der Zee, K.G. (author), Van Brummelen, E.H. (author), De Borst, R. (author)In free-boundary problems, the accuracy of a goal quantity of interest depends on both the accuracy of the approximate solution and the accuracy of the domain approximation. We develop duality-based a posteriori error estimates for functional outputs of solutions of free-boundary problems that include both sources of error. The derivation of an...journal article 2010
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Van der Zee, K.G. (author), Van Brummelen, E.H. (author), De Borst, R. (author)Coercivity of the bilinear form in a continuum variational problem is a fundamental property for finite-element discretizations: By the classical Lax–Milgram theorem, any conforming discretization of a coercive variational problem is stable; i.e., discrete approximations are well-posed and possess unique solutions, irrespective of the specifics...journal article 2006
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Van der Zee, K.G. (author), Van Brummelen, E.H. (author), De Borst, R. (author)Numerical simulations of fluid-structure interaction typically require vast computational resources. Finite-element techniques employing goal-oriented hp-adaptation strategies could offer a substantial improvement in the efficiency of such simulations. These strategies rely on dual-based a-posteriori error estimates for quantities of interest....conference paper 2006
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Van der Zee, K.G. (author), Van Brummelen, E.H. (author), De Borst, R. (author)Numerical simulations of fluid-structure interaction typically require vast computational resources. Finite-element techniques employing goal-oriented hp-adaptation strategies could offer a substantial improvement in the efficiency of such simulations. These strategies rely on dual-based a-posteriori error estimates for quantities of interest....conference paper 2006
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Michler, C. (author), Van Brummelen, E.H. (author), In 't Groen, R. (author), De Borst, R. (author)The numerical solution of fluid-structure interactions with the customary subiteration method incurs numerous deficiencies. We validate a recently proposed solution method based on the conjugation of subiteration with a Newton-Krylov method, and demonstrate its superiority and beneficial characteristics.conference paper 2006
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De Borst, R. (author), Hulshoff, S.J. (author), Lenz, S. (author), Munts, E.A. (author), Van Brummelen, E.H. (author), Wall, W.A. (author)The basic idea of multiscale methods, namely the decomposition of a problem into a coarse scale and a fine scale, has in an intuitive manner been used in engineering for many decades, if not for centuries. Also in computational science, large-scale problems have been solved, and local data, for instance displacements, forces or velocities, have...conference paper 2006
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Michler, C. (author), Van Brummelen, E.H. (author), In 't Groen, R. (author), De Borst, R. (author)The numerical solution of fluid-structure interactions with the customary subiteration method incurs numerous deficiencies. We validate a recently proposed solution method based on the conjugation of subiteration with a Newton-Krylov method, and demonstrate its superiority and beneficial characteristics.conference paper 2006
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De Borst, R. (author), Hulshoff, S.J. (author), Lenz, S. (author), Munts, E.A. (author), Van Brummelen, E.H. (author), Wall, W.A. (author)The basic idea of multiscale methods, namely the decomposition of a problem into a coarse scale and a fine scale, has in an intuitive manner been used in engineering for many decades, if not for centuries. Also in computational science, large-scale problems have been solved, and local data, for instance displacements, forces or velocities, have...conference paper 2006
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Van Brummelen, E.H. (author), Van der Zee, K.G. (author), De Borst, R. (author)The basic iterative method for solving fluid-structure-interaction problems is a defect-correction process based on a partitioning of the underlying operator into a fluid part and a structural part. In the present work we establish for a prototypical model problem that this defect-correction process yields an excellent smoother for multigrid, on...report 2006
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Van Brummelen, E.H. (author), Michler, C. (author), De Borst, R. (author)Subiteration forms the basic iterative method for solving the aggregated equations in fluid-structure-interaction problems, in which the fluid and structure equations are solved alternately subject to complementary partitions of the interface conditions. However, this subiteration process can be defective or inadequate, as it is endowed with...report 2005
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Remmers, J.J.C. (author), De Borst, R. (author), Needleman, A. (author)A numerical method for crack growth is described in which the crack is not regarded as a single discontinuity that propagates continuously. Instead, the crack is represented by a set of overlapping cohesive segments. These cohesive segments are inserted into finite elements as discontinuities in the displacement field by exploiting the partition...journal article 2003
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Meijers, S.J.H. (author), Bijen, J.M.J.M. (author), De Borst, R. (author), Fraaij, A.L.A. (author)Exposure to a saline environment is a major threat with respect to the durability of reinforced concrete structures. The chloride ions, which are present in seawater and de-icing salts, are able to penetrate the concrete up to the depth of the reinforcement. They can eventually trigger a pitting corrosion process. The assessment of a corrosion...journal article 2001
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Suiker, A.S.J. (author), Metrikine, A.V. (author), De Borst, R. (author)This paper discusses the steady state response of a rigidly supported, granular layer to a moving load. Accordingly, the dynamic behaviour of a ballast layer under an instantaneous train axle passage is simulated, where the rigid support reflects a substratum that is much stiffer than the ballast layer, e.g. ballast in a concrete railway tunnel...journal article 2000
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Van Zijl, G.P.A.G. (author), De Borst, R. (author), Rots, J.G. (author)The response of cementitious materials is highly time dependent. On the one hand, it can lead to delayed collapse of structures fabricated of such materials. On the other hand, the time dependence is associated with the relaxation of peak stresses, which avoids, or postpones damage. A finite element formulation is presented for the analysis of...journal article 2000
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Hashagen, F. (author), De Borst, R. (author)In this contribution numerical models are discussed for describing failure mechanisms in fibre metal laminates. Fibre metal laminates form a new class of materials which are considered for a possible application to the fuselage of future aircraft generations. The intensive experimental analyses of these materials are focused on the assessment of...journal article 1998
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- Lourenco, P.B. (author), De Borst, R. (author), Rots, J.G. (author) journal article 1997
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- Wang, W.M. (author), Sluys, L.J. (author), De Borst, R. (author) journal article 1997
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- Hashagen, F. (author), De Borst, R. (author) journal article 1997
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- De Borst, R. (author) journal article 1997