On the Finite Element Method for Mixed Variational Inequalities Arising in Elastoplasticity

We analyze the finite-element method for a class of mixed variational inequalities of the second kind, which arises in elastoplastic problems. An abstract variational inequality, of which the elastoplastic problems are special cases, has been previously introduced and analyzed [B. D. Reddy, Nonlinear Anal., 19 (1992), pp. 1071-1089], and existence and uniqueness results for this problem have been given there. In this contribution the same approach is taken ; that is, finite-element approximations of the abstract variational inequality are analyzed, and the results are then discussed in further detail in the context of the concrete problems. Results on convergence are presented, as are error estimates. Regularization methods are commonly employed in variational inequalities of this kind, in both theoretical and computational investigations. We derive a posteriori error estimates which enable us to determine whether the solution of a regularized problem can be taken as a sufficiently accurate approximation of the solution of the original problem

Some aspects of dynamic computational modelling of direct current plasma arc phenomena

Direct current arc furnaces see considerable use in modern industrial melting and smelting processes. Pyrometallurgical applications for this type of furnace are wide-ranging, and include commodities such as Ferrochrome, Ferronickel, Cobalt, Zinc, Magnesium, Titanium Dioxide, Platinum-group metals1, and others. Central to the operation of such furnaces is the direct current plasma arc, a sustained high temperature jet of ionised gas which is formed between the end of one or more graphite electrodes and the bath of molten process material below. Passage of electric current through the arc inputs energy and maintains the high temperatures necessary for ionisation via ohmic heating. This is balanced by various mechanisms of energy loss from the arc, including volumetric radiation and convection to the molten bath surface below. Much of this energy is delivered to a localised area directly beneath the arc, making it a very efficient means of heating the process material. Flow of plasma in the arc column is driven strongly by electromagnetic Lorentz forces resulting from the constriction of the conduction channel in the vicinity of the electrode. This constriction causes the arc to draw in gas from the surroundings and accelerate it away from the electrode surface, toward the molten bath below (the Maecker effect2). Much research has been conducted in the area of numerical modelling of arc phenomena, starting with Szekely and co-workers3 and becoming increasingly more sophisticated with the advent of better software, property data, and increased computing capability. However, the majority of arc modelling efforts concentrate on steady-state, axisymmetric systems. While valuable from an engineering standpoint these models are not able to describe any transient behaviour exhibited by the arc, or any evolution of the shape and structure of the arc which breaks the symmetry imposed by the model. Both of these aspects are important for a deeper understanding of direct current plasma arc behaviour

A priori error analysis of virtual element method for contact problem

As an extension of the finite element method, the virtual element method (VEM) can handle very general polygonal meshes, making it very suitable for non-matching meshes. In (Wriggers et al. in Comput. Mech. 58:1039–1050, 2016), the lowest-order virtual element method was applied to solve the contact problem of two elastic bodies on non-matching meshes. The numerical experiments showed the robustness and accuracy of the virtual element scheme. In this paper, we establish a priori error estimate of the virtual element method for the contact problem and prove that the lowest-order VEM achieves linear convergence order, which is optimal

Convergence in the incompressible limit of new discontinuous Galerkin methods with general quadrilateral and hexahedral elements

Standard low-order finite elements, which perform well for problems involving compressible elastic materials, are known to under-perform when nearly incompressible materials are involved, commonly exhibiting the locking phenomenon. Interior penalty (IP) discontinuous Galerkin methods have been shown to circumvent locking when simplicial elements are used. The same IP methods, however, result in locking on meshes of quadrilaterals. The authors have shown in earlier work that under-integration of specified terms in the IP formulation eliminates the locking problem for rectangular elements. Here it is demonstrated through an extensive numerical investigation that the effect of using under-integration carries over successfully to meshes of more general quadrilateral elements, as would likely be used in practical applications, and results in accurate displacement approximations. Uniform convergence with respect to the compressibility parameter is shown numerically. Additionally, a stress approximation obtained here by postprocessing shows good convergence in the incompressible limit

Global patient outcomes after elective surgery: prospective cohort study in 27 low-, middle- and high-income countries.

BACKGROUND: As global initiatives increase patient access to surgical treatments, there remains a need to understand the adverse effects of surgery and define appropriate levels of perioperative care. METHODS: We designed a prospective international 7-day cohort study of outcomes following elective adult inpatient surgery in 27 countries. The primary outcome was in-hospital complications. Secondary outcomes were death following a complication (failure to rescue) and death in hospital. Process measures were admission to critical care immediately after surgery or to treat a complication and duration of hospital stay. A single definition of critical care was used for all countries. RESULTS: A total of 474 hospitals in 19 high-, 7 middle- and 1 low-income country were included in the primary analysis. Data included 44 814 patients with a median hospital stay of 4 (range 2-7) days. A total of 7508 patients (16.8%) developed one or more postoperative complication and 207 died (0.5%). The overall mortality among patients who developed complications was 2.8%. Mortality following complications ranged from 2.4% for pulmonary embolism to 43.9% for cardiac arrest. A total of 4360 (9.7%) patients were admitted to a critical care unit as routine immediately after surgery, of whom 2198 (50.4%) developed a complication, with 105 (2.4%) deaths. A total of 1233 patients (16.4%) were admitted to a critical care unit to treat complications, with 119 (9.7%) deaths. Despite lower baseline risk, outcomes were similar in low- and middle-income compared with high-income countries. CONCLUSIONS: Poor patient outcomes are common after inpatient surgery. Global initiatives to increase access to surgical treatments should also address the need for safe perioperative care. STUDY REGISTRATION: ISRCTN5181700

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2–4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease