A posteriori error analysis in finite elements: The element residual method for symmetrizable problems with applications to compressible euler and Navier-stokes equations

Oden, J. T.; Demkowicz, Leszek; Westermann, Tim

doi:10.1016/0045-7825(90)90164-h

Cited by 38 publications

(10 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We shall study a general class of compressible flow equa- [27][28][29]. The capabilities offered by the adaptive proce-tions of the form dures were early recognized [30,21], and intensive investigations in the area have continued for the last decade [31].…”

Section: And the Entropy Functionmentioning

confidence: 99%

Entropy Controlled Adaptive Finite Element Simulations for Compressible Gas Flow

Banaś

Demkowicz

1996

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

Section: And the Entropy Functionmentioning

confidence: 99%

Entropy Controlled Adaptive Finite Element Simulations for Compressible Gas Flow

Banaś

Demkowicz

1996

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

“…Several error indicators have been suggested in the literature for time-dependent calculations (for example, see articles by Lohner [7] and Oden et al [8]). Our aim here is not to compare the different error indicators reported in the literature, but to use one of them to demonstrate the implementation of our methodology.…”

Section: Introductionmentioning

confidence: 98%

Parallel computation of unsteady compressible flows with the EDICT

Mittal

Aliabadi

Tezduyar

1999

Computational Mechanics

View full text Add to dashboard Cite

Recently, the Enhanced-Discretization InterfaceCapturing Technique (EDICT) was introduced for simulation of unsteady¯ow problems with interfaces such as two-¯uid and free-surface¯ows. The EDICT yields increased accuracy in representing the interface. Here we extend the EDICT to simulation of unsteady viscous compressible¯ows with boundary/shear layers and shock/ expansion waves. The purpose is to increase the accuracy in selected regions of the computational domain. An error indicator is used to identify these regions that need enhanced discretization. Stabilized ®nite-element formulations are employed to solve the Navier-Stokes equations in their conservation law form. The ®nite element functions corresponding to enhanced discretization are designed to have two components, with each component coming from a different level of mesh re®nement over the same computational domain. The primary component comes from a base mesh. A subset of the elements in this base mesh are identi®ed for enhanced discretization by utilizing the error indicator. A secondary, more re®ned, mesh is constructed by patching together the second-level meshes generated over this subset of elements, and the second component of the functions comes from this mesh. The subset of elements in the base mesh that form the secondary mesh may change from one time level to other depending on the distribution of the error in the computations.Using a parallel implementation of this EDICT-based method, we apply it to test problems with shocks and boundary layers, and demonstrate that this method can be used very effectively to increase the accuracy of the base ®nite element formulation. IntroductionRecently, Tezduyar et al.[1] introduced the EnhancedDiscretization Interface-Capturing Technique (EDICT) for simulation of unsteady¯ow problems with interfaces such as two-¯uid and free-surface¯ows. The starting point for the EDICT is the volume of¯uid (VOF) method [2]. In the EDICT, the Navier-Stokes equations are solved over a nonmoving mesh and an interface function, with two distinct values that serves as a marker identifying the two¯uids, is transported with a time-dependent advection equation. To increase the accuracy in representing the interface, function spaces corresponding to enhanced discretization are used at and near the interface.In this article we extend the EDICT to unsteady compressible¯ows with shock/expansion waves, boundary/ shear layers, and their interactions. Our target is to increase the accuracy in selected regions of the computational domain. These regions are identi®ed by an error indicator. The Navier-Stokes equations of compressiblē ows in their conservation law form are solved using a stabilized ®nite element formulation based on conservation variables. The streamline-upwind/Petrov-Galerkin (SUPG) stabilization technique is employed to stabilize the computations against potential numerical oscillations in advection dominated¯ows [3,4,5]. A shock-capturing term is added to the formulation to provide stability to the computations in the...

show abstract

“…Limited work has been done using a posteriori error estimates in the context of mesh movement for one-dimensional problems [1,8], but to our knowledge, such strategies have not been attempted in higher dimensions. (While our concern is parabolic problems, it is worth noting that global error estimation for hyperbolic problems is also complicated by the combination of local time and space discretization errors [29,30], although in certain cases success in solving the error estimation problem globally is achieved [22]. )…”

Section: Introductionmentioning

confidence: 99%