Stabilised finite element methods for the Oseen problem on anisotropic quadrilateral meshes

In this work we present and analyse new inf-sup stable, and stabilised, finite element methods for the Oseen equation in anisotropic quadrilateral meshes. The meshes are formed of closed parallelograms, and the analysis is restricted to two space dimensions. Starting with the lowest order QIn this work we present and analyse new inf-sup stable, and stabilised, finite element methods for the Oseen equation in anisotropic quadrilateral meshes. The meshes are formed of closed parallelograms, and the analysis is restricted to two space dimensions. Starting with the lowest order Q2 1 × P0 pair, we first identify the pressure components that make this finite element pair to be non-inf-sup stable, especially with respect to the aspect ratio. We then propose a way to penalise them, both strongly, by directly removing them from the space, and weakly, by adding a stabilisation term based on jumps of the pressure across selected edges. Concerning the velocity stabilisation, we propose an enhanced grad-div term. Stability and optimal a priori error estimates are given, and the results are confirmed numerically. Q21 × P0 pair, we first identify the pressure components that make this finite element pair to be non-inf-sup stable, especially with respect to the aspect ratio. We then propose a way to penalise them, both strongly, by directly removing them from the space, and weakly, by adding a stabilisation term based on jumps of the pressure across selected edges. Concerning the velocity stabilisation, we propose an enhanced grad-div term. Stability and optimal a priori error estimates are given, and the results are confirmed numerically

Stabilisation of high aspect ratio mixed finite elements for incompressible flow

Anisotropically refined mixed finite elements are beneficial for the resolution of local features such as boundary layers. Unfortunately, the stability of the resulting scheme is highly sensitive to the aspect ratio of the elements. Previous analysis revealed that the degeneration arises from a relatively small number of spurious (piecewise constant) pressure modes. The present article is concerned with resolving the problem of how to suppress the spurious pressure modes in order to restore stability yet at the same time not incur any deterioration in the approximation properties of the reduced pressure space. Two results are presented. The first gives the minimal constraints on the pressure space needed to restore stability with respect to aspect ratio and shows that the approximation properties of the constrained pressure space and the unconstrained pressure space are essentially identical. Alternatively, one can impose the constraint weakly through the use of a stabilized finite element scheme. A second result shows that the stabilized finite element scheme is robust with respect to the aspect ratio of the elements and produces an approximation that satisfies an error bound of the same type to the mixed finite element scheme using the constrained space

Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model

This work presents new stabilised finite element methods for a bending moments formulation of the Reissner-Mindlin plate model. The introduction of the bending moment as an extra unknown leads to a new weak formulation, where the symmetry of this variable is imposed strongly in the space. This weak problem is proved to be well-posed, and stabilised Galerkin schemes for its discretisation are presented and analysed. The finite element methods are such that the bending moment tensor is sought in a finite element space constituted of piecewise linear continuos and symmetric tensors. Optimal error estimates are proved, and these findings are illustrated by representative numerical experiments

A note on the stabilised Q1-P0 method on quadrilaterals with high aspect ratios

This work deals with the stabilisation of mixed methods for the Stokes problem on anisotropic meshes. For this, we extend a method proposed previously in Liao and Silvester (IMA J Numer Anal 33(2):413-431, 2013), to cover the case in which the mesh contains anisotropically refined corners. This modification consists of adding extra jump terms in selected edges connecting small shape regular with large anisotropic elements. We prove stability and convergence of the proposed method, and provide numerical evidence for the fact that our approach successfully removes the dependence on the anisotropy

Antirheumatic drug response signatures in human chondrocytes: potential molecular targets to stimulate cartilage regeneration

Rheumatoid arthritis (RA) leads to progressive destruction of articular cartilage. This study aimed to disclose major mechanisms of antirheumatic drug action on human chondrocytes and to reveal marker and pharmacological target genes that are involved in cartilage dysfunction and regeneration

Clinicopathologic and molecular analysis of embryonal rhabdomyosarcoma of the genitourinary tract: evidence for a distinct DICER1-associated subgroup.

Embryonal rhabdomyosarcoma (ERMS) of the uterus has recently been shown to frequently harbor DICER1 mutations. Interestingly, only rare cases of extrauterine DICER1-associated ERMS, mostly located in the genitourinary tract, have been reported to date. Our goal was to study clinicopathologic and molecular profiles of DICER1-mutant (DICER1-mut) and DICER1-wild type (DICER1-wt) ERMS in a cohort of genitourinary tumors. We collected a cohort of 17 ERMS including nine uterine (four uterine corpus and five cervix), one vaginal, and seven urinary tract tumors. DNA sequencing revealed mutations of DICER1 in 9/9 uterine ERMS. All other ERMS of our cohort were DICER1-wt. The median age at diagnosis of patients with DICER1-mut and DICER1-wt ERMS was 36 years and 5 years, respectively. Limited follow-up data (available for 15/17 patients) suggested that DICER1-mut ERMS might show a less aggressive clinical course than DICER1-wt ERMS. Histological features only observed in DICER1-mut ERMS were cartilaginous nodules (6/9 DICER1-mut ERMS), in one case accompanied by foci of ossification. Recurrent mutations identified in both DICER1-mut and DICER1-wt ERMS affected KRAS, NRAS, and TP53. Copy number analysis revealed similar structural variations with frequent gains on chromosomes 2, 3, and 8, independent of DICER1 mutation status. Unsupervised hierarchical clustering of array-based whole-genome DNA methylation data of our study cohort together with an extended methylation data set including different RMS subtypes from genitourinary and extra-genitourinary locations (n = 102), revealed a distinct cluster for DICER1-mut ERMS. Such tumors clearly segregated from the clusters of DICER1-wt ERMS, alveolar RMS, and MYOD1-mutant spindle cell and sclerosing RMS. Only one tumor, previously diagnosed as ERMS arising in the maxilla of a 6-year-old boy clustered with DICER1-mut ERMS of the uterus. Subsequent sequencing analysis identified two DICER1 mutations in the latter case. Our results suggest that DICER1-mut ERMS might qualify as a distinct subtype in future classifications of RMS

Stabilised mixed finite element methods on anisotropic meshes

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