High order limiters remain one of the main challenges for discontinuous Galerkin (DG) methods in solving hyperbolic conservation laws. This paper proposes an efficient limiting procedure for the DG method. The key feature is to construct additional polynomials from the solutions on neighboring cells by means of secondary reconstruction. Then the limited solution on current cell can be obtained ...

We demonstrate the advantages of using multi-reolution analysis with multiwavelet basis with the Discontinuous Galerkin (DG) method. This provides significant enhancements to the standard DG methods. To illustrate the important gains of using the Multiwavelet DG method we apply it to conservation and convection diffusion problems in multiple dimensions. The significant benefits of merging DG me...

In this paper, an analysis of the accuracy-enhancement for the discontinuous Galerkin (DG) method applied to one-dimensional scalar nonlinear hyperbolic conservation laws is carried out. This requires analyzing the divided difference of the errors for the DG solution. We therefore first prove that the [Formula: see text]-th order [Formula: see text] divided difference of the DG error in the [Fo...

The discontinuous Galerkin (dG) method outputs a sequence of polynomial pieces. Post-processing the sequence by Smoothness-Increasing Accuracy-Conserving (SIAC) convolution not only increases the smoothness of the sequence but can also improve its accuracy and yield superconvergence. SIAC convolution is considered optimal if the SIAC kernels, in the form of a linear combination of B-splines of ...

In this paper, we reformulate the piecewise linear discontinuous Galerkin (DG) method for solving two dimensional steady state scalar conservation laws in the framework of residual distribution (RD) schemes. This allows us to propose a new class of nonlinear stabilization that does not destroy the formal accuracy of the schemes. Numerical results are shown to demonstrate the behavior of this ap...

In this paper we present a thorough set of numerical experiments to confirm the robustness of several Discontinuous Galerkin (DG) methods proposed for the approximation of Darcy law. We perform fairly twoand three-dimensional tests involving both low and high order approximations. Convergence tests carried out on Cartesian grids as well as on structured and unstructured triangular grids confirm...

Background The role of surgery in treating children with functional constipation (FC) is controversial, because of the efficacy of bowel management programs. This case series is comprised of failures: 43 children, spanning 25 years' practice, who had megarectosigmoid (MRS) and unremitting constipation. Purpose To determine whether these children were helped by surgery, and to contribute to fo...

A 5-year-old girl was referred because of recurrent watery diarrhea, abdominal pain, and flatulence. She was the second of 3 children. Her 10-year-old sister was normally developed and healthy. Her younger brother has meningomyelocele and hydrocephalus. At 1 year of age, the patient was admitted to the hospital for recurrent bronchitis, otitis media, food refusal, mild diarrhea, and abdominal d...

Objectives: Our objective was to perform a cross-sectional research to measure the prevalence of bipolar mood disorder (BMD) in Iranian children and adolescents and its comorbidity with psychiatric disorders. Also, the main purpose of this study was to characterize the main risk factors for BMD in children and adolescents. Method: This work was an analytical cross-sectional study. In a communi...

BACKGROUND Behavioral aberrations such as nail biting, finger sucking, and pica have been postulated as risk factors that enhance helminths ova transmission. These aberrations may present commonly in children with chronic neurological disorders and predispose them to heavy intensity of intestinal helminthiasis. This comparative cross-sectional study was to determine the prevalence, intensity, a...