EP.WE.709A local experience of non-operative management for an appendicitis cohort during COVID-19

Background During the first United Kingdom COVID-19 wave, the Royal Colleges of Surgeons initially recommended conservative management with antibiotics instead of surgery for appendicitis. This study compared local outcomes of appendicitis during this period with a pre-COVID-19 cohort. Methods An observational study was conducted in a district general hospital. All episodes of appendicitis were prospectively studied from 25th March 2020 until 26th May 2020 and compared with a retrospective pre-COVID cohort from 27th November 2019 until 29th January 2020. Primary outcome was 30-day treatment failure of simple appendicitis for conservatively managed cases during COVID-19 compared to surgically managed cases pre-pandemic. Treatment failure was defined as any unplanned radiological or surgical intervention. Results Over nine weeks, there were 39 cases of appendicitis during COVID-19 and 50 cases pre-COVID-19. Twenty-six and 50 cases underwent appendicectomy during and pre-COVID-19 respectively. There was no difference in 30-day postoperative complication rates and nor were there any peri-operative COVID-19 infections. Twelve cases of simple appendicitis underwent conservative management during COVID-19 and were compared with 23 operatively managed simple cases pre-pandemic. There was a higher failure rate in the conservative versus operative group (33.3 vs 0% OR = 24.88, 95% CI 1.21 to 512.9, p = 0.0095). Length of stay was similar (1.5 vs 2.0 p = 0.576). Discussion Locally, conservative management was more likely to fail than initial appendicectomy. We suggest that surgery should remain first line for appendicitis, with conservative management reserved for those with suspected or proven COVID-19 infection.

Enriched Galerkin method for the shallow-water equations

This work presents an enriched Galerkin (EG) discretization for the two-dimensional shallow-water equations. The EG finite element spaces are obtained by extending the approximation spaces of the classical finite elements by discontinuous functions supported on elements. The simplest EG space is constructed by enriching the piecewise linear continuous Galerkin space with discontinuous, element-wise constant functions. Similar to discontinuous Galerkin (DG) discretizations, the EG scheme is locally conservative, while, in multiple space dimensions, the EG space is significantly smaller than that of the DG method. This implies a lower number of degrees of freedom compared to the DG method. The EG discretization presented for the shallow-water equations is well-balanced, in the sense that it preserves lake-at-rest configurations. We evaluate the method’s robustness and accuracy using various analytical and realistic problems and compare the results to those obtained using the DG method. Finally, we briefly discuss implementation aspects of the EG method within our MATLAB / GNU Octave framework FESTUNG.

A lowest-order staggered DG method for the coupled Stokes–Darcy problem

In this paper we propose a locally conservative, lowest-order staggered discontinuous Galerkin method for the coupled Stokes–Darcy problem on general quadrilateral and polygonal meshes. This model is composed of Stokes flow in the fluid region and Darcy flow in the porous media region, coupling together through mass conservation, balance of normal forces and the Beavers–Joseph–Saffman condition. Stability of the proposed method is proved. A new regularization operator is constructed to show the discrete trace inequality. Optimal convergence estimates for all the approximations covering low regularity are achieved. Numerical experiments are given to illustrate the performances of the proposed method. The numerical results indicate that the proposed method can be flexibly applied to rough grids such as the trapezoidal grid and $h$-perturbation grid.