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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multiscale finite element methods: ideas and challenges
多尺度 有限元方法 思路 挑战
2023/5/6
Multiscale phenomena significantly impact on the computation and modeling for scientific and engineering problems. Multiscale finite element methods are used to build reduced order computational model...
G1 Spline Surface Construction By Geometric Partial Differential Equations Using Mixed Finite Element Methods
Spline surface Discretizations GPDE Convergence
2012/8/8
Variational formulations of three fourth order geometric partial di甧rential equations are
derived, and based on which mixed 痭ite element methods are presented for constructing
G1 smooth B-spline sur...
Multiscale Asymptotic Expansion and Finite Element Methods For the Mixed Boundary Value Problems of Second Order Elliptic Equation in Perforated Domains
Homogenization Multiscale asymptotic expansion Elliptic equationof second order with rapidly oscillating coefficients Perforated domain
2012/8/8
In this paper, we will discuss the mixed boundary value problems for
the second order elliptic equation with rapidly oscillating coefficients in perforated
domains, and will present the higher-order...
Dual Formulations of Mixed Finite Element Methods
Dual Formulations Mixed Finite Element Methods
2011/2/22
Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be store...
When parametric functions are used to blend 3D surfaces, geometric
continuity of displacements and derivatives until to the surface
boundary must be satisfied. By the traditional blending techniqu...
Least-Squares Mixed Finite Element Methods for the Incompressible Magnetohydrodynamic Equations
2007/12/12
Least-squares mixed finite element methods are proposed and analyzed for the incompressible magnetohydrodynamic equations, where the two vorticities are additionally introduced as independent variable...
For coupled system of multilayer dynamics of fluids in porousmedia, the characteristic alternating-direction finite elementmethods for nonrectangular regions applicable to parallelarithmetic are put f...
We develop the interpolated finite element method to solve second-order hyperbolic equations. The standard linear finite element solution is used to generate a newsolution by quadratic interpolation o...
EXTRAPOLATION FOR FINITE ELEMENT METHODS OF THE FIRST KIND FREDHOLM INTEGRAL EQUATIONS
Extrapolation finite element method Fred
2007/8/7
In this paper,a numerical analysis of finite element methods for Fredholm equations of the first kind, which is based upon regularization, is made. It shows that extrapolation algorithms can accelerat...