A note on a priori $$\mathbf {L^p}$$Lp-error estimates for the obstacle problem
Sign Up to like & getrecommendations! Published in 2018 at "Numerische Mathematik"
DOI: 10.1007/s00211-017-0931-5
Abstract: This paper is concerned with a priori error estimates for the piecewise linear finite element approximation of the classical obstacle problem. We demonstrate by means of two one-dimensional counterexamples that the $$L^2$$L2-error between the exact… read more here.
Keywords: note priori; obstacle problem; error estimates; priori mathbf ... See more keywords
Asymptotically Exact Posteriori Error Estimates for the Local Discontinuous Galerkin Method Applied to Nonlinear Convection–Diffusion Problems
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-018-0687-9
Abstract: In this paper, we present and analyze implicit a posteriori error estimates for the local discontinuous Galerkin (LDG) method applied to nonlinear convection–diffusion problems in one space dimension. Optimal a priori error estimates for the… read more here.
Keywords: estimates local; error; local discontinuous; solution ... See more keywords
A Priori Error Estimates for State-Constrained Semilinear Parabolic Optimal Control Problems
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DOI: 10.1007/s10957-018-1311-8
Abstract: We consider the finite element discretization of semilinear parabolic optimization problems subject to pointwise in time constraints on mean values of the state variable. In order to control the feasibility violation induced by the discretization,… read more here.
Keywords: semilinear parabolic; state; control; optimization ... See more keywords
Aspects of an adaptive finite element method for the fractional Laplacian: A priori and a posteriori error estimates, efficient implementation and multigrid solver☆☆☆
Sign Up to like & getrecommendations! Published in 2017 at "Computer Methods in Applied Mechanics and Engineering"
DOI: 10.1016/j.cma.2017.08.019
Abstract: Abstract We develop all of the components needed to construct an adaptive finite element code that can be used to approximate fractional partial differential equations, on non-trivial domains in d ≥ 1 dimensions. Our main… read more here.
Keywords: finite element; adaptive finite; error estimates; error ... See more keywords
A posteriori error estimates for Biot system using Enriched Galerkin for flow
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DOI: 10.1016/j.cma.2020.113185
Abstract: Abstract We analyze the Biot system solved with a fixed-stress split, Enriched Galerkin (EG) discretization for the flow equation, and Galerkin for the mechanics equation. Residual-based a posteriori error estimates are established with both lower… read more here.
Keywords: enriched galerkin; error; error estimates; posteriori error ... See more keywords
Explicit k-dependence for P k finite elements in W m,p error estimates: application to probabilistic laws for accuracy analysis
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DOI: 10.1080/00036811.2019.1698727
Abstract: We derive an explicit k-dependence in error estimates for Lagrange finite elements. Two laws of probability are established to measure the relative accuracy between and finite elements, ( ), in terms of -norms. We further… read more here.
Keywords: finite elements; error estimates; explicit dependence; probabilistic laws ... See more keywords
A Posteriori Error Estimates for Lumped Mass Finite Element Method for Linear Parabolic Problems Using Elliptic Reconstruction
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DOI: 10.1080/01630563.2017.1338730
Abstract: ABSTRACT We study residual-based a posteriori error estimates for both the spatially discrete and the fully discrete lumped mass finite element approximation for parabolic problems in a bounded convex polygonal domain in ℝ2. In particular,… read more here.
Keywords: finite element; posteriori error; lumped mass; error estimates ... See more keywords
Dynamical approximations for composite quantum systems:Assessment of error estimates for a separable ansatz
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/ac6841
Abstract: Numerical studies are presented to assess error estimates for a separable (Hartree) approximation for dynamically evolving composite quantum systems which exhibit distinct scales defined by their mass and frequency ratios. The relevant error estimates were… read more here.
Keywords: dynamical approximations; composite quantum; error estimates; error ... See more keywords
Error Estimates of Local Energy Regularization for the Logarithmic Schrodinger Equation
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DOI: 10.1142/s0218202522500038
Abstract: The logarithmic nonlinearity has been used in many partial differential equations (PDEs) for modeling problems in various applications. Due to the singularity of the logarithmic function, it introduces tremendous difficulties in establishing mathematical theories, as… read more here.
Keywords: energy; local energy; regularization; equation ... See more keywords
A Priori and a Posteriori Error Estimates of a WOPSIP DG Method for the Heat Equation
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Problems in Engineering"
DOI: 10.1155/2020/7525676
Abstract: We introduce and analyze a weakly overpenalized symmetric interior penalty method for solving the heat equation. We first provide optimal a priori error estimates in the energy norm for the fully discrete scheme with backward… read more here.
Keywords: error; method; heat equation; error estimates ... See more keywords
A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Inequalities and Applications"
DOI: 10.1186/s13660-018-1729-4
Abstract: In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete spectral… read more here.
Keywords: control; control problem; nonlinear parabolic; error estimates ... See more keywords