A class of nonparametric DSSY nonconforming quadrilateral elements

A new class of nonparametric nonconforming quadrilateral finite elements is introduced which has the midpoint continuity and the mean value continuity at the interfaces of elements simultaneously as the rectangular DSSY element [J.Douglas, Jr., J. E. Santos, D. Sheen, and X. Ye. Nonconforming {G}alerkin methods based on quadrilateral elements for second order elliptic problems. ESAIM--Math. Model. Numer. Anal., 33(4):747--770, 1999]. The parametric DSSY element for general quadrilaterals requires five degrees of freedom to have an optimal order of convergence [Z. Cai, J. Douglas, Jr., J. E. Santos, D. Sheen, and X. Ye. Nonconforming quadrilateral finite elements: A correction. Calcolo, 37(4):253--254, 2000], while the new nonparametric DSSY elements require only four degrees of freedom. The design of new elements is based on the decomposition of a bilinear transform into a simple bilinear map followed by a suitable affine map. Numerical results are presented to compare the new elements with the parametric DSSY element.Comment: 20 page

Discrete qualocation methods for logarithmic-kernel integral equations on a piecewise smooth boundary

We consider a fully discrete qualocation method for Symm's integral equation. The method is that of Sloan and Burn [14], for which a complete analysis is available in the case of smooth curves. The convergence for smooth curves can be improved by a subtraction of singularity (Jeon and Kimn [10]). In this paper we extend these results for smooth boundaries to polygonal boundaries. The analysis uses a mesh grading transformation method for Symm's integral equation, as in Elschner and Graham [4] and Elschner and Stephan [7], to overcome the singular behavior of solutions at corners

The collocation method for mixed boundary value problems on domains with curved polygonal boundaries

We consider an indirect boundary integral equation formulation for the mixed Dirichlet Neumann boundary value problem for the Laplace equation on a plane domain with a polygonal boundary. The resulting system of integral equations is solved by a collocation method which uses a mesh grading transformation and a cosine approximating space. The mesh grading transformation method yields fast convergence of the collocation solution by smoothing the singularities of the exact solution. A complete stability and solvability analysis of the transformed integral equations is given by use of a Mellin transform technique, in a setting in which each arc of the polygon has associated with it a periodic Sobolev space

Treatment shortening of drug-sensitive pulmonary tuberculosis using high-dose rifampicin for 3 months after culture conversion (Hi-DoRi-3): a study protocol for an open-label randomized clinical trial

Background : The standard treatment regimen for drug-sensitive tuberculosis (TB), comprising four companion drugs, requires a minimum duration of 6 months, and this lengthy treatment leads to poor adherence and increased toxicity. To improve rates of adherence, reduce adverse events, and lower costs, a simplified and shortened treatment regimen is warranted. Methods : This study is a multicenter, open-label randomized clinical trial of non-inferiority design that compares a new regimen with the conventional regimen for drug-sensitive pulmonary TB. The investigational group will use a regimen of high-dose rifampicin (30 mg/kg/day) with isoniazid and pyrazinamide, and the treatment will be maintained for 12 weeks after the achievement of negative conversion of sputum culture. The control group will be treated for 6 months with a World Health Organization-endorsed regimen consisting of isoniazid, rifampicin (10 mg/kg/day), ethambutol, and pyrazinamide. The primary endpoint is the proportion of unfavorable outcomes at 18 months after randomization. Secondary outcomes include time to unfavorable treatment outcome, time to culture conversion on liquid medium, treatment success rate at the end of treatment, proportion of recurrence at 18 months after randomization, time to recurrence after treatment completion, and adverse events of grade 3 or higher during the treatment. We predict a 10% unfavorable outcome for the control group, and 0% difference from the investigational group. Based on 80% verification power and a 2.5% one-sided significance level for a non-inferiority margin of 6%, 393 participants per group are required. Considering the 15% dropout rate, a total of 926 participants (463 in each group) will be recruited. Discussion : This study will inform on the feasibility of the treatment regimen using high-dose rifampicin with a shortened and individualized treatment duration for pulmonary TB. Trial registration : ClinicalTrials.gov NCT04485156.Registered on July 24, 2020.This work was supported by a grant from the Korea National Institute of Health (2020-ER5201-01), Republic of Korea. High-dose rifampicin tablets and capsules were donated from Yuhan (Seoul, Republic of Korea) for this study. The funder and donor had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript

A flux preserving immersed nonconforming finite element method for elliptic problems

An immersed nonconforming finite element method based on the flux continuity on intercell boundaries is introduced. The direct application of flux continuity across the support of basis functions yields a nonsymmetric stiffness system for interface elements. To overcome non-symmetry of the stiffness system we introduce a modification based on the Riesz representation and a local postprocessing to recover local fluxes. This approach yields a P 1 immersed nonconforming finite element method with a slightly different source term from the standard nonconforming finite element method. The recovered numerical flux conserves total flux in arbitrary sub-domain. An optimal rate of convergence in the energy norm is obtained and numerical examples are provided to confirm our analysis

Automatic Boundary Integral Equation Programs For The Planar Laplace Equation

Algorithms with automatic error control are described for the solution of Laplace's equation on both interior and exterior regions, with both Dirichlet and Neumann boundary conditions. The algorithms are based on standard reformulations of each boundary value problem as a boundary integral equation of the second kind. The Nyström method is used to solve the integral equations, and convergence of arbitrary high order is observed when the boundary data is analytic. The Kelvin transformation is introduced to allow a simple conversion between internal and external problems. Two Fortran program implementations, DRCHLT and NEUMAN, are defined, analyzed, and illustrated