Electronic Research Archive, 2023 In this paper, we present a two-grid scheme of fully discrete finite element approximation for optimal control problems governed by parabolic integro-differential equations. The state and co-state variables are approximated by a piecewise linear function
Changling Xu , Huilai Li
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Robust error estimates in weak norms for advection dominated transport problems with rough data [PDF]
, 2014 We consider mixing problems in the form of transient convection--diffusion equations with a velocity vector field with multiscale character and rough data.
Burman, Erik
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Finite Element Error Analysis of a Viscoelastic Timoshenko Beam with Thermodiffusion Effects
Mathematics, 2023 In this paper, a thermomechanical problem involving a viscoelastic Timoshenko beam is analyzed from a numerical point of view. The so-called thermodiffusion effects are also included in the model. The problem is written as a linear system composed of two
Jacobo G. Baldonedo +3 more
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Numerical analysis of a relaxed variational model of hysteresis in two-phase solids [PDF]
, 2001 This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al.
Ball +11 more
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Error estimates of finite volume method for Stokes optimal control problem
Journal of Inequalities and Applications, 2021 In this paper, we discuss a priori error estimates for the finite volume element approximation of optimal control problem governed by Stokes equations. Under some reasonable assumptions, we obtain optimal L 2 $L^{2}$ -norm error estimates.
Lin Lan +4 more
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Discontinuous Finite Element Methods for Interface Problems: Robust A Priori and A Posteriori Error Estimates [PDF]
, 2017 For elliptic interface problems in two and three dimensions, this paper studies a priori and residual-based a posteriori error estimations for the Crouzeix–Raviart nonconforming and the discontinuous Galerkin finite element approximations.
Cai, Z, He, C, Zhang, S
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A priori error estimation for the stochastic perturbation method
Computer Methods in Applied Mechanics and Engineering, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiang-Yu Wang +3 more
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A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems
Journal of Applied Mathematics, 2013 A novel characteristic expanded mixed finite element method is proposed and analyzed for reaction-convection-diffusion problems. The diffusion term ∇·(a(x,t)∇u) is discretized by the novel expanded mixed method, whose gradient belongs to the square ...
Yang Liu +4 more
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Error estimates of a semi-discrete LDG method for the system of damped acoustic wave equation
Advances in Difference Equations, 2018 We consider a system of acoustic wave equation possessing lower-order perturbation terms in a bounded domain in R2 $\mathbb{R}^{2}$. In this paper, we show the system is well-posed and stable with energy decays introducing a local discontinuous Galerkin (
Dojin Kim
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A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation
The Scientific World Journal, 2014 We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen’s expanded mixed element method.
Jinfeng Wang +3 more
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