Space‐time finite elements and an adaptive strategy for the coupled thermoelasticity problem

Larsson, Fredrik; Hansbo, Peter; Runesson, Kenneth

doi:10.1002/nme.563

Cited by 17 publications

(11 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Johnson et al [9][10][11], Rannacher et al [4,[12][13][14], Ramm et al [5,6,15], Oden and Prudhomme [16,17] and R uter et al [18,19]. Recent contributions are those of Larsson et al [7,20,21] dealing with problems of coupled thermoelasticity, non-linear elasticity and viscoplasticity. A major advantage of the proposed approach is that it is possible to choose any goal-oriented error measure (in spacetime), which is of engineering interest, and the data of the dual problem are chosen accordingly in such a fashion that an exact error representation can be obtained (at least formally).…”

Section: Introductionmentioning

confidence: 95%

Time finite elements and error computation for (visco)plasticity with hardening or softening

Larsson

Runesson

Hansbo

2003

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYIn this paper we investigate the possibility for, and characteristics of, reliable and e cient a posteriori error computation at the integration of the constitutive relations pertinent to (visco)plasticity with softening=hardening. The variational structure admits the use of ÿnite elements in time, which are based on the Discontinuous Galerkin method. An important feature is the possibility to select 'goal-oriented' error measures with great freedom. A key task is to identify and solve an auxiliary problem, that is the dual of the actual (primal) problem. Di erent strategies for computing the dual solution accurately, yet avoiding excessive cost, are investigated in the paper. In particular, we consider the characteristics at the limit of rate-independent plasticity.

show abstract

Section: Introductionmentioning

confidence: 95%

Time finite elements and error computation for (visco)plasticity with hardening or softening

Larsson

Runesson

Hansbo

2003

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…Obviously, we also can involve adaptive strategies into the present coupled space-time finite element scheme. Besides coupled space-time strategies based on duality techniques [31,62,63] simple temporal error indicators based on the jump terms [34,35,64] can be motivated. Within a system of differential algebraic equation (DAE) there usually exits an optimal time-step length.…”

Section: Dynamic Response Of a Soil Column Under A Step Loadingmentioning

confidence: 99%

A time-discontinuous Galerkin method for the dynamical analysis of porous media

Chen

Steeb

Diebels

2006

Int. J. Numer. Anal. Meth. Geomech.

View full text Add to dashboard Cite

SUMMARYWe present a time-discontinuous Galerkin method (DGT) for the dynamic analysis of fully saturated porous media. The numerical method consists of a finite element discretization in space and time. The discrete basis functions are continuous in space and discontinuous in time. The continuity across the time interval is weakly enforced by a flux function. Two applications and several numerical investigations confirm the quality of the proposed space-time finite element scheme.

show abstract

“…One important advantage of a FE-approximation in time is the strait-forward possibility for global error control in space-time, cf. [5]. This global error control is not applicable using the more classical finite-difference schemes.…”

Section: Weak Formulationmentioning

confidence: 99%

“…Specializing the formulation in (24), (25) to the first order continuous Galerkin, cG(1), in time: 5 Superscript • (j) denotes iteration j.…”

Section: Continuous Galerkin (Cg) For Non-linear Diffusionmentioning

confidence: 99%

Space-time finite elements for a simplified thermo-metallurgical problem relevant to casting

2006

View full text Add to dashboard Cite

The non-linear thermo-metallurgical problem, relevant for the cooling of a molten metal including the macro-segregation that occurs during the cooling process, is studied here. Due to the strong non-linearities involved in phase transformations, it is necessary to use a fine resolution in space-time in a finite element approximation in order to meet accuracy requirements. We derive space-time FE-methods based on the discontinuous and continuous Galerkin method in time for the energy equation. This formulation integrates the stored energy exactly for a given heat flux. When macro-segregation is incorporated into the model, the problem can be formulated in such a way that the phase-transition drives a flow of species. In addition, diffusion is possible throughout the domain. The model can be further rewritten using a potential approach. By this approach for modelling macro-segregation, we are able to obtain discretizations that guarantee that the balance equations are satisfied, and it is possible to solve the phase-transition problem either as a field problem or as a local problem (defined by a local evolution rule).

show abstract

Space‐time finite elements and an adaptive strategy for the coupled thermoelasticity problem

Cited by 17 publications

References 8 publications

Time finite elements and error computation for (visco)plasticity with hardening or softening

Time finite elements and error computation for (visco)plasticity with hardening or softening

A time-discontinuous Galerkin method for the dynamical analysis of porous media

Space-time finite elements for a simplified thermo-metallurgical problem relevant to casting

Contact Info

Product

Resources

About