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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Unconditional stability and error estimates of FEMs for the electro-osmotic flow in micro-channels
微通道 电渗流FEM 无条件稳定性 误差估计
2023/5/15
In this paper, we will provide the the finite element method for the electro-osmotic flow in micro-channels, in which a convection-diffusion type equation is given for the charge density ρe. A time-di...
ELLIPTIC RECONSTRUCTION AND A POSTERIORI ERROR ESTIMATES FOR PARABOLIC PROBLEMS
A posteriori error estimators fi nite elements semidiscrete parabolic problems
2015/12/11
It is known that the energy technique for a posteriori error analysis
of finite element discretizations of parabolic problems yields suboptimal rates
in the norm L1(0; T;L2
(Ω)): In thi...
GALERKIN AND RUNGE{KUTTA METHODS: UNIFIED FORMULATION, A POSTERIORI ERROR ESTIMATES AND NODAL SUPERCONVERGENCE
Continuous discontinuous Galerkin methods
2015/12/11
We unify the formulation and analysis of Galerkin and Runge{Kutta
methods for the time discretization of parabolic equations. This, together with
the concept of reconstruction of the approximate sol...
Optimal order a posteriori error estimates for a class of Runge{Kutta and Galerkin methods
error estimates Galerkin methods
2015/12/11
We derive a posteriori error estimates, which exhibit
optimal global order, for a class of time stepping methods of any
order that include Runge{Kutta Collocation (RK-C) methods and
the continuous ...
POINTWISE A POSTERIORI ERROR ESTIMATES FOR MONOTONE SEMI-LINEAR EQUATIONS
residual maximum norm
2015/12/11
We derive upper and lower a posteriori estimates for the maximum norm error in nite element solutions of monotone semi-linear equations.
The estimates hold for Lagrange elements of any xed order, n...
Polyharmonic Hardy Spaces on the Complexified Annulus and Error Estimates of Cubature Formulas
Hardy space Numerical Integration Cubature formulas Error estimate
2012/4/23
The present paper has a twofold contribution: first, we introduce a new concept of Hardy spaces on a multidimensional complexified annular domain which is closely related to the annulus of the Klein-D...
A Posteriori Error Estimates for Nonconforming Approximations of Evolutionary Convection-Diffusion Problems
a posteriori error estimates time-nonconforming approximations convection-diffusion
2011/2/25
We derive computable upper bounds for the difference between an exact solution of the evolutionary convection-diffusion problem and an approximation of this solution.
Error Estimates in Horocycle Averages Asymptotics: Challenges from String Theory
Error Estimates Horocycle Averages Asymptotics Challenges String Theory
2011/1/21
For modular functions of rapid decay, a classical result connects the error estimate in their long horocycle average asymptotic to the Riemann hy-pothesis.
A posteriori error estimates for a finite element approximation of transmission problems with sign changing coefficients
A posteriori estimator non positive definite diffusion problems
2010/12/8
We perform the a posteriori error analysis of residual type of a transmission problem with sign changing coefficients. According to [6] if the contrast is large enough, the continuous problem can be t...
The Optimal Order Error Estimates for Finite Element Approximations to Hyperbolic Problems
2007/12/12
In this paper, the linear finite element approximation to the positive and symmetric, linear hyperbolic systems is analyzed and an $O(h^2)$ order error estimate is established under the conditions of ...
We examine a simple averaging formula for the gradient
of linear finite elements in $R^d$ whose interpolation order
in the $L^q$-norm is $\Cal O(h^2)$ for $d<2q$ and nonuniform
triangulations. For ...
Construction of Solutions and L^1-error Estimates of Viscous Methods for Scalar Conservation Laws with Boundary
scalar conservation laws initial boundary value problem global weak entropy solution error estimate of viscous methods
2007/12/11
This paper is concerned with an initial boundary value problem for strictly convex conservation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many d...
Korovkin Type Error Estimates for Positive Linear Operators Involving Some Special Functions
Positive linear operators Korovkin-Bohman theorem Bernstein power series generating function, Pochhammer symbol hypergeometric function Peetre´ s K-functional first and second order modulus of continuities functional differential equation
2010/2/25
In the present paper, we introduce a new sequence of linear positive operators with the help of generating functions. We obtain some Korovkin type approximation properties for these operators and comp...