Stability analysis of a finite element scheme for the heat equation with a random initial condition

1981 ◽  
Vol 29 (1) ◽  
pp. 109-113 ◽  
Author(s):  
Sciichi Tasaka
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Heat Equation ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Finite Element Scheme ◽  
Element Scheme

scholarly journals Mixed Weak Galerkin Method for Heat Equation with Random Initial Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Chenguang Zhou ◽  
Yongkui Zou ◽  
Shimin Chai ◽  
Fengshan Zhang
Keyword(s):  
Finite Element ◽  
Heat Equation ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Optimal Order ◽  
Random Initial Condition ◽  
Initial Condition ◽  
Polynomial Functions ◽  
Weak Galerkin ◽  
Convergence Estimates

This paper is devoted to the numerical analysis of weak Galerkin mixed finite element method (WGMFEM) for solving a heat equation with random initial condition. To set up the finite element spaces, we choose piecewise continuous polynomial functions of degree j+1 with j≥0 for the primary variables and piecewise discontinuous vector-valued polynomial functions of degree j for the flux ones. We further establish the stability analysis of both semidiscrete and fully discrete WGMFE schemes. In addition, we prove the optimal order convergence estimates in L2 norm for scalar solutions and triple-bar norm for vector solutions and statistical variance-type convergence estimates. Ultimately, we provide a few numerical experiments to illustrate the efficiency of the proposed schemes and theoretical analysis.

scholarly journals Superconvergence of finite element method for parabolic problem

2000 ◽  
Vol 23 (8) ◽  
pp. 567-578 ◽  
Author(s):  
Do Y. Kwak ◽  
Sungyun Lee ◽  
Qian Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parabolic Problem ◽  
Higher Order ◽  
Initial Condition ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Discrete Finite Element ◽  
Element Method

We study superconvergence of a semi-discrete finite element scheme for parabolic problem. Our new scheme is based on introducing different approximation of initial condition. First, we give a superconvergence ofuh−Rhu, then use a postprocessing to improve the accuracy to higher order.

An adaptive finite element scheme to solve fluid-structure vibration problems on non-matching grids

2001 ◽  
Vol 4 (2) ◽  
pp. 67-78 ◽  
Author(s):  
Ana Alonso ◽  
Anahí Dello Russo ◽  
César Otero-Souto ◽  
Claudio Padra ◽  
Rodolfo Rodríguez
Keyword(s):  
Finite Element ◽  
Adaptive Finite Element ◽  
Finite Element Scheme ◽  
Fluid Structure ◽  
Element Scheme ◽  
Structure Vibration ◽  
Vibration Problems
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