Convergence and Error Analysis of Fully Discrete Iterative Coupling Schemes for Coupling Flow with Geomechanics

2016 ◽  
Author(s):  
T. Almani ◽  
K. Kumar ◽  
G. Singh ◽  
M. Wheeler
Keyword(s):  
Error Analysis ◽  
Iterative Coupling ◽  
Fully Discrete

Convergence and error analysis of fully discrete iterative coupling schemes for coupling flow with geomechanics

2017 ◽  
Vol 21 (5-6) ◽  
pp. 1157-1172 ◽  
Author(s):  
T. Almani ◽  
K. Kumar ◽  
M. F. Wheeler
Keyword(s):  
Error Analysis ◽  
Iterative Coupling ◽  
Fully Discrete

Error Analysis of an Unconditionally Energy Stable Local Discontinuous Galerkin Scheme for the Cahn–Hilliard Equation with Concentration-Dependent Mobility

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Fengna Yan ◽  
Yan Xu
Keyword(s):  
Error Analysis ◽  
Discontinuous Galerkin ◽  
Implicit Time ◽  
Time Step ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Hilliard Equation ◽  
Local Discontinuous Galerkin ◽  
Energy Stable ◽  
Cahn Hilliard Equation

Abstract In this paper, we mainly study the error analysis of an unconditionally energy stable local discontinuous Galerkin (LDG) scheme for the Cahn–Hilliard equation with concentration-dependent mobility. The time discretization is based on the invariant energy quadratization (IEQ) method. The fully discrete scheme leads to a linear algebraic system to solve at each time step. The main difficulty in the error estimates is the lack of control on some jump terms at cell boundaries in the LDG discretization. Special treatments are needed for the initial condition and the non-constant mobility term of the Cahn–Hilliard equation. For the analysis of the non-constant mobility term, we take full advantage of the semi-implicit time-discrete method and bound some numerical variables in L ∞ L^{\infty} -norm by the mathematical induction method. The optimal error results are obtained for the fully discrete scheme.

scholarly journals Resolvent estimates of elliptic differential and finite-element operators in pairs of function spaces

2004 ◽  
Vol 2004 (5) ◽  
pp. 217-238 ◽  
Author(s):  
Nikolai Yu. Bakaev
Keyword(s):  
Finite Element ◽  
Error Analysis ◽  
Function Spaces ◽  
Resolvent Estimates ◽  
Discrete Approximations ◽  
Partial Differential ◽  
Fully Discrete ◽  
The Stability ◽  
Stability And Error Analysis

We present some resolvent estimates of elliptic differential and finite-element operators in pairs of function spaces, for which the first space in a pair is endowed with stronger norm. In this work we deal with estimates in (Lebesgue, Lebesgue), (Hölder, Lebesgue), and (Hölder, Hölder) pairs of norms. In particular, our results are useful for the stability and error analysis of semidiscrete and fully discrete approximations to parabolic partial differential problems with rough and distribution-valued data.

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