Strong Convergence of a Fully Discrete Scheme for Multiplicative Noise Driving SPDEs with Non-Globally Lipschitz Continuous Coefficients

2021 ◽  
Vol 14 (4) ◽  
pp. 1085-1109
Author(s):  
Xu Yang & Weidong Zhao
Keyword(s):  
Strong Convergence ◽  
Multiplicative Noise ◽  
Lipschitz Continuous ◽  
Discrete Scheme ◽  
Fully Discrete

Semi-Discrete and Fully Discrete Hybrid Stress Finite Element Methods for Elastodynamic Problems

2015 ◽  
Vol 8 (4) ◽  
pp. 582-604
Author(s):  
Zhengqin Yu ◽  
Xiaoping Xie
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Stability Result ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Quadrilateral Finite Element ◽  
Hybrid Stress Finite Element ◽  
Hybrid Stress

AbstractThis paper proposes and analyzes semi-discrete and fully discrete hybrid stress finite element methods for elastodynamic problems. A hybrid stress quadrilateral finite element approximation is used in the space directions. A second-order center difference is adopted in the time direction for the fully discrete scheme. Error estimates of the two schemes, as well as a stability result for the fully discrete scheme, are derived. Numerical experiments are done to verify the theoretical results.

NUMERICAL ANALYSIS OF A MINIMAX OPTIMAL CONTROL PROBLEM WITH AN ADDITIVE FINAL COST

2002 ◽  
Vol 12 (02) ◽  
pp. 183-203 ◽  
Author(s):  
LAURA S. ARAGONE ◽  
SILVIA C. DI MARCO ◽  
ROBERTO L. V. GONZÁLEZ
Keyword(s):  
Optimal Control ◽  
Numerical Analysis ◽  
Optimal Control Problem ◽  
Convergence Rate ◽  
Control Problem ◽  
Discrete Solution ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Minimax Optimal Control ◽  
Continuous Problem

In this paper we deal with the numerical analysis of an optimal control problem of minimax type with finite horizon and final cost. To get numerical approximations we devise here a fully discrete scheme which enables us to compute an approximated solution. We prove that the fully discrete solution converges to the solution of the continuous problem and we also give the order of the convergence rate. Finally we present some numerical results.

scholarly journals AN H1 -GALERKIN MIXED FINITE ELEMENT APPROXIMATION OF A NONLOCAL HYPERBOLIC EQUATION

2017 ◽  
Vol 22 (5) ◽  
pp. 643-653
Author(s):  
Fengxin Chen ◽  
Zhaojie Zhou
Keyword(s):  
Finite Element ◽  
Hyperbolic Equation ◽  
Mixed Finite Element ◽  
A Priori ◽  
Finite Element Approximation ◽  
Nonlinear Hyperbolic Equation ◽  
Element Approximation ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Priori Error Estimates

In this paper we investigate a semi-discrete H1 -Galerkin mixed finite element approximation of one kind of nolocal second order nonlinear hyperbolic equation, which is often used to describe vibration of an elastic string. A priori error estimates for the semi-discrete scheme are derived. A fully discrete scheme is constructed and one numerical example is given to verify the theoretical findings.

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