Masahisa Tabata

TL;DR: In this article, the authors found that Escherichia coli, Bacteroides and Clostridium often found in the biliary tract may contribute to the formation of bile pigment calcium stones by producing beta-glucuronidase and deconjugating bilirubin diglucuronide to form free unconjugated bilirus, which in turn combines with calcium, leading to stone formation.

TL;DR: In this paper, the authors studied two-point boundary value problems for two-component systems with a small parameter and showed that the reduced problem has multiple solutions, and the singular perturbation method is used for constructing large amplitude solutions of the original problem.

TL;DR: A new characteristic finite element scheme is presented that is of second order accuracy in time increment, symmetric, and unconditionally stable and optimal error estimates are proved in the framework of L^2-theory.

Abstract: The purpose ofthis paper is to present a new class of upwind finite element schemes for convective diffusion équations and to gwe error analysis These schemes based on an intégral formula have the following advantages (i) They are effective particularly in the case when the convection is dominated^ (n) Solutions obtained by them satisfy a discrete conservation law, (in) Solutions obtained by a scheme with a particuîar choice satisfy a discrete maximum principle {under suitable conditions) We show that the finite element solutions converge to the exact one with rate 0(h) in L(Q, T, H (Q)) and L (0,T,L(a)) Resumé — Le but de cet article est de présenter une classe nouvelle de schémas d'éléments finis conservatîfs et décentres pour des équations de diffusion avec convection, et de donner des estimations d*erreur Les schémas, qui sont basés sur une formule intégrale, ont les avantages suivants (î) Ils sont effectifs surtout dans le cas où la convection est dominante, (n) Des solutions obtenues par eux satisfont a une loi de conservation discrète, (ni) Des solutions obtenues par un schéma particulier satisfont au principe du maximum discret (sous des conditions convenables) On montre que les solutions obtenues par éléments finis convergent vers la solution exacte en 0(h) dans L(0, T, H 1 ^ ) ) et L°°{0, T, L(H)) INTRODUCTION Consider the convective diffusion équation in Q x ( 0 J ) , (0.1) (*) Reçu le 16 novembre 1979 {) Technical System center, Mitsubishi Heavy Industry, Ltd, Kobe, Japan () Department of Mathematics, Kyoto Umversity, Kyoto, Japan R A I R O Analyse numénque/Numencal Analysis, 0399-0516/1981/3/$ 5 00 © Bordas-Dunod 4 K. BABA, M. TABATA where Q is a bounded domain in U. The solution u{x, t) of (0.1) subject to the free boundary condition d^-b.vu = 0 on ÔQ x (0, T) satisfies the mass-conservation law f u(x, t)dx= f M°(X) dx + f A f /(x, 0 j=Q WTM(Q) = { u ; u is measurable in Q, \\ u \\m>PtQ < + oo } , H(Q) = For 0 < a ^ 1 and a non-negative integer m, « L,oc,n = sup { | Dl u(x)\; \ P | = m, x e Q } , m II w i l m a n = E Iwb.oo.n» j=o II « llm+^oca = II u L,oo,n + I u l«+ot,oo,n > C(Q) = { u ; u is continuously differentiable up to order m in Q } , C(Q) = {u;ue C(Q), || W ||m+aj00)n < + oo } . Let X be a Banach space with norm || . ||x. C(0, T ; X) = { u ; u is continuously differentiable up to order m as a function from [0, T] into X } , II u \\C^O,T;X) = £ max { || D/ w(0 | |x ; t e [0, T]}, j=0

TL;DR: General error estimates are proved for a class of finite element schemes for nonstationary thermal convection problems with temperature-dependent coefficients that turn the diffusion and the buoyancy terms to be nonlinear, which increases the nonlinearity of the problems.