共查询到20条相似文献,搜索用时 656 毫秒
1.
We introduce modified Lagrange–Galerkin (MLG) methods of order one and two with respect to time to integrate convection–diffusion
equations. As numerical tests show, the new methods are more efficient, but maintaining the same order of convergence, than
the conventional Lagrange–Galerkin (LG) methods when they are used with either P
1 or P
2 finite elements. The error analysis reveals that: (1) when the problem is diffusion dominated the convergence of the modified
LG methods is of the form O(h
m+1 + h
2 + Δt
q
), q = 1 or 2 and m being the degree of the polynomials of the finite elements; (2) when the problem is convection dominated and the time step
Δt is large enough the convergence is of the form
O(\frachm+1Dt+h2+Dtq){O(\frac{h^{m+1}}{\Delta t}+h^{2}+\Delta t^{q})} ; (3) as in case (2) but with Δt small, then the order of convergence is now O(h
m
+ h
2 + Δt
q
); (4) when the problem is convection dominated the convergence is uniform with respect to the diffusion parameter ν (x, t), so that when ν → 0 and the forcing term is also equal to zero the error tends to that of the pure convection problem. Our error analysis
shows that the conventional LG methods exhibit the same error behavior as the MLG methods but without the term h
2. Numerical experiments support these theoretical results. 相似文献
2.
Bart De Bruyn 《Annals of Combinatorics》2010,14(3):307-318
Let f be an isometric embedding of the dual polar space ${\Delta = DQ(2n, {\mathbb K})}Let f be an isometric embedding of the dual polar space
D = DQ(2n, \mathbb K){\Delta = DQ(2n, {\mathbb K})} into
D¢ = DQ(2n, \mathbb K¢){\Delta^\prime = DQ(2n, {\mathbb K}^\prime)}. Let P denote the point-set of Δ and let
e¢: D¢? S¢ @ PG(2n - 1, \mathbb K¢){e^\prime : \Delta^\prime \rightarrow {\Sigma^\prime} \cong {\rm PG}(2^n - 1, {{\mathbb K}^\prime})} denote the spin-embedding of Δ′. We show that for every locally singular hyperplane H of Δ, there exists a unique locally singular hyperplane H′ of Δ′ such that f(H) = f(P) ?H¢{f(H) = f(P) \cap H^\prime}. We use this to show that there exists a subgeometry
S @ PG(2n - 1, \mathbb K){\Sigma \cong {\rm PG}(2^n - 1, {\mathbb K})} of Σ′ such that: (i) e¢°f (x) ? S{e^\prime \circ f (x) \in \Sigma} for every point x of D; (ii) e : = e¢°f{\Delta; ({\rm ii})\,e := e^\prime \circ f} defines a full embedding of Δ into Σ, which is isomorphic to the spin-embedding of Δ. 相似文献
3.
Manuel Blickle Karl Schwede Shunsuke Takagi Wenliang Zhang 《Mathematische Annalen》2010,347(4):917-949
We prove that the F-jumping numbers of the test ideal
t(X; D, \mathfrakat){\tau(X; \Delta, \mathfrak{a}^t)} are discrete and rational under the assumptions that X is a normal and F-finite scheme over a field of positive characteristic p, K
X
+ Δ is
\mathbb Q{\mathbb {Q}}-Cartier of index not divisible p, and either X is essentially of finite type over a field or the sheaf of ideals
\mathfraka{\mathfrak{a}} is locally principal. This is the largest generality for which discreteness and rationality are known for the jumping numbers
of multiplier ideals in characteristic zero. 相似文献
4.
The aim of this study is to prove global existence of classical solutions for systems of the form ${\frac{\partial u}{\partial t} -a \Delta u=-f(u,v)}The aim of this study is to prove global existence of classical solutions for systems of the form
\frac?u?t -a Du=-f(u,v){\frac{\partial u}{\partial t} -a \Delta u=-f(u,v)} ,
\frac?v?t -b Dv=g(u,v){\frac{\partial v}{\partial t} -b \Delta v=g(u,v)} in (0, +∞) × Ω where Ω is an open bounded domain of class C
1 in
\mathbbRn{\mathbb{R}^n}, a > 0, b > 0 and f, g are nonnegative continuously differentiable functions on [0, +∞) × [0, +∞) satisfying f (0, η) = 0, g(x,h) £ C j(x)eahb{g(\xi,\eta) \leq C \varphi(\xi)e^{\alpha {\eta^\beta}}} and g(ξ, η) ≤ ψ(η)f(ξ, η) for some constants C > 0, α > 0 and β ≥ 1 where j{\varphi} and ψ are any nonnegative continuously differentiable functions on [0, +∞) such that j(0)=0{\varphi(0)=0} and limh? +¥hb-1y(h) = l{ \lim_{\eta \rightarrow +\infty}\eta^{\beta -1}\psi(\eta)= \ell} where ℓ is a nonnegative constant. The asymptotic behavior of the global solutions as t goes to +∞ is also studied. For this purpose, we use the appropriate techniques which are based on semigroups, energy estimates
and Lyapunov functional methods. 相似文献
5.
John R. Akeroyd 《Arkiv f?r Matematik》2011,49(1):1-16
It is shown that for any t, 0<t<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that
G\{1} í \mathbbD:={z:|z| < 1}\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:|z|<1\}
and with the property that the analytic polynomials are dense in the Bergman space
\mathbbAt(\mathbbD\G)\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma)
. It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous
real-valued function on [0,1], where the polynomials are dense in
Ht(\mathbbD\G)H^{t}(\mathbb{D}\setminus\Gamma)
; improving upon a result in an earlier paper. 相似文献
6.
Changchun Liu 《Monatshefte für Mathematik》2012,94(3):237-249
In this paper, we study the initial-boundary value problem of porous medium equation ρ(x)u
t
= Δu
m
+ V(x)h(t)u
p
in a cone D = (0, ∞) × Ω, where V(x) ~ |x|s, h(t) ~ ts{V(x)\,{\sim}\, |x|^\sigma, h(t)\,{\sim}\, t^s}. Let ω
1 denote the smallest Dirichlet eigenvalue for the Laplace-Beltrami operator on Ω and let l denote the positive root of l
2 + (n − 2)l = ω
1. We prove that if
m < p £ 1+(m-1)(1+s)+\frac2(s+1)+sn+l{m < p \leq 1+(m-1)(1+s)+\frac{2(s+1)+\sigma}{n+l}}, then the problem has no global nonnegative solutions for any nonnegative u
0 unless u
0 = 0; if ${p >1 +(m-1)(1+s)+\frac{2(s+1)+\sigma}{n+l}}${p >1 +(m-1)(1+s)+\frac{2(s+1)+\sigma}{n+l}}, then the problem has global solutions for some u
0 ≥ 0. 相似文献
7.
Y. Guo 《Ukrainian Mathematical Journal》2011,62(9):1409-1419
We consider the existence of nontrivial solutions of the boundary-value problems for nonlinear fractional differential equations
*20c Da u(t) + l[ f( t,u(t) ) + q(t) ] = 0, 0 < t < 1, u(0) = 0, u(1) = bu(h), \begin{array}{*{20}{c}} {{{\mathbf{D}}^\alpha }u(t) + {{\lambda }}\left[ {f\left( {t,u(t)} \right) + q(t)} \right] = 0,\quad 0 < t < 1,} \\ {u(0) = 0,\quad u(1) = \beta u(\eta ),} \\ \end{array} 相似文献
8.
Changxing Miao Liutang Xue 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(6):707-735
In this paper we consider the following 2D Boussinesq–Navier–Stokes systems
|