Finite element analysis for a regularized variational inequality of the second kind

Zhang, Tie; Zhang, Shuhua; Azari, Hossein

Displaying similar documents to “Finite element analysis for a regularized variational inequality of the second kind”

Explicit estimation of error constants appearing in non-conforming linear triangular finite element method

Xuefeng Liu, Fumio Kikuchi (2018)

Applications of Mathematics

Similarity:

The non-conforming linear ( $P_{1}$ ) triangular FEM can be viewed as a kind of the discontinuous Galerkin method, and is attractive in both the theoretical and practical purposes. Since various error constants must be quantitatively evaluated for its accurate a priori and a posteriori error estimates, we derive their theoretical upper bounds and some computational results. In particular, the Babuška-Aziz maximum angle condition is required just as in the case of the conforming $P_{1}$ triangle. Some...

On some a posteriori error estimation results for the method of lines

Segeth, Karel, Šolín, Pavel

Similarity:

The paper is an attempt to present an (incomplete) historical survey of some basic results of residual type estimation procedures from the beginning of their development through contemporary results to future prospects. Recently we witness a rapidly increasing use of the $h p$ -FEM which is due to the well-established theory. However, the conventional a posteriori error estimates (in the form of a single number per element) are not enough here, more complex estimates are needed, and this...

On polynomial robustness of flux reconstructions

Miloslav Vlasák (2020)

Applications of Mathematics

Similarity:

We deal with the numerical solution of elliptic not necessarily self-adjoint problems. We derive a posteriori upper bound based on the flux reconstruction that can be directly and cheaply evaluated from the original fluxes and we show for one-dimensional problems that local efficiency of the resulting a posteriori error estimators depends on $p^{1 / 2}$ only, where $p$ is the discretization polynomial degree. The theoretical results are verified by numerical experiments.

Nonconforming P1 elements on distorted triangulations: Lower bounds for the discrete energy norm error

Peter Oswald (2017)

Applications of Mathematics

Similarity:

Compared to conforming P1 finite elements, nonconforming P1 finite element discretizations are thought to be less sensitive to the appearance of distorted triangulations. E.g., optimal-order discrete $H^{1}$ norm best approximation error estimates for $H^{2}$ functions hold for arbitrary triangulations. However, the constants in similar estimates for the error of the Galerkin projection for second-order elliptic problems show a dependence on the maximum angle of all triangles in the triangulation....

Explicit estimates for the summatory function of Λ(n)/n from the one of Λ(n)

Olivier Ramaré (2013)

Acta Arithmetica

Similarity:

We prove that the error term $\sum_{n \leq x} Λ (n) / n - l o g x + γ$ differs from (ψ(x)-x)/x by a well controlled function. We deduce very precise numerical results from the formula obtained.

Anisotropic $h p$ -adaptive method based on interpolation error estimates in the $H^{1}$ -seminorm

Vít Dolejší (2015)

Applications of Mathematics

Similarity:

We develop a new technique which, for the given smooth function, generates the anisotropic triangular grid and the corresponding polynomial approximation degrees based on the minimization of the interpolation error in the broken $H^{1}$ -seminorm. This technique can be employed for the numerical solution of boundary value problems with the aid of finite element methods. We present the theoretical background of this approach and show several numerical examples demonstrating the efficiency of...

New a posteriori $L^{\infty} (L^{2})$ and $L^{2} (L^{2})$ -error estimates of mixed finite element methods for general nonlinear parabolic optimal control problems

Zuliang Lu (2016)

Applications of Mathematics

Similarity:

We study new a posteriori error estimates of the mixed finite element methods for general optimal control problems governed by nonlinear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates in $L^{\infty} (J; L^{2} (Ω))$ -norm and $L^{2} (J; L^{2} (Ω))$ -norm for both the state, the co-state and the control approximation. Such estimates, which seem to be new,...

Unified error analysis of discontinuous Galerkin methods for parabolic obstacle problem

Papri Majumder (2021)

Applications of Mathematics

Similarity:

We introduce and study various discontinuous Galerkin (DG) finite element approximations for a parabolic variational inequality associated with a general obstacle problem in $ℝ^{d}$ $(d = 2, 3)$ . For the fully-discrete DG scheme, we employ a piecewise linear finite element space for spatial discretization, whereas the time discretization is carried out with the implicit backward Euler method. We present a unified error analysis for all well known symmetric and non-symmetric DG fully discrete...