Robust a posteriori error estimators for mixed approximation of nearly incompressible elasticity

This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori error estimators for the energy norm of the finite element error are proposed and analysed. We establish upper and lower bounds for the energy error in terms of the proposed error estimators and prove that the constants in the bounds are independent of the Lam\'{e} coefficients: thus the proposed estimators are robust in the incompressible limit. Numerical results are presented that validate the theoretical estimates. The software used to generate these results is available online.Comment: 23 pages, 9 figure

Finite element approximation for a delayed generalized Burgers-Huxley equation with weakly singular kernels: Part I Well-posedness, Regularity and Conforming approximation

The analysis of a delayed generalized Burgers-Huxley equation (a non-linear advection-diffusion-reaction problem) with weakly singular kernels is carried out in this work. Moreover, numerical approximations are performed using the conforming finite element method (CFEM). The existence, uniqueness and regularity results for the continuous problem have been discussed in detail using the Faedo-Galerkin approximation technique. For the numerical studies, we first propose a semi-discrete conforming finite element scheme for space discretization and discuss its error estimates under minimal regularity assumptions. We then employ a backward Euler discretization in time and CFEM in space to obtain a fully-discrete approximation. Additionally, we derive a prior error estimates for the fully-discrete approximated solution. Finally, we present computational results that support the derived theoretical results

Drug utilisation evaluation in patients with osteoarthritis in tertiary care hospital

Background: The principle aim of our study is to assess the prescribing pattern of drugs used in treatment of osteoarthritis patients. Methods: A prospective and empirical study was carried out at department of orthopaedics-Shadan teaching and general hospital, for 6 months.Results: During the study period, a total 120 patients were enrolled, of which 57% were females, 43% were males and common age group was ≥60 years. It was found that 56% of OA patient have history of trauma and 62% of obese individual contribute to occurrence of OA. It was found that subjects developed comorbidities like CV disorders which is 36%. It was found that 63% have OA for a duration of >2 years, 56% had no knowledge about their medications, 59% have co-morbidity, 61% have treatment complexity. NSAID’s, calcium, vitamin D3, glucosamine and chondroitin sulphate were the most frequently prescribed drugs in OA accounting for 50%. It was reported that 55% were adherent to OA medication, adherence to physical activity was 64%, adherence to weight loss was 62%.Conclusions: Our study manifest that majority of the patients had duration of >2 years of OA. The reasons for the uncontrolled pain was due to absence of awareness about osteoarthritis-related difficulties, drugs, low calcium diet, increased stress, obesity, and advanced age. Continuous health education, patient counselling, information about medication adherence and satisfaction at follow-ups is essential to avoid the problems