Related papers: Scaling-robust built-in a posteriori error estimat…
We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in [40], enables the use of separate meshes to…
In this paper, we propose and analyze the least squares finite element methods for the linear elasticity interface problem in the stress-displacement system on unfitted meshes. We consider the cases that the interface is $C^2$ or polygonal,…
The realization of a standard Adaptive Finite Element Method (AFEM) preserves the mesh conformity by performing a completion step in the refinement loop: in addition to elements marked for refinement due to their contribution to the global…
The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
In this paper we develop a new a posteriori error analysis for the Monge-Amp\`ere equation approximated by conforming finite element method on isotropic meshes in 2D. The approach utilizes a slight variant of the mixed discretization…
In this paper, a few dual least-squares finite element methods and their application to scalar linear hyperbolic problems are studied. The purpose is to obtain $L^2$-norm approximations on finite element spaces of the exact solutions to…
We consider a least-squares variational kernel-based method for numerical solution of second order elliptic partial differential equations on a multi-dimensional domain. In this setting it is not assumed that the differential operator is…
A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions are proposed. Stability and efficiency of the estimators are proved. Finally, we provide…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
An element based adaptation method is developed for an anisotropic a posteriori error estimator. The adaptation does not make use of a metric, but instead equidistributes the error over elements using local mesh modifications. Numerical…
In this study, we present a novel stabilized finite element analysis for transient Stokes model. The algebraic subgrid multiscale approach has been employed to arrive at the stabilized coupled variational formulation. Derivation of the…
We propose two classes of mixed finite elements for linear elasticity of any order, with interior penalty for nonconforming symmetric stress approximation. One key point of our method is to introduce some appropriate nonconforming…
We propose and analyze a posteriori error estimators for an optimal control problem that involves an elliptic partial differential equation as state equation and a control variable that enters the state equation as a coefficient; pointwise…
The classical continuous mixed formulation of linear elasticity with pointwise symmetric stresses allows for a conforming finite element discretization with piecewise polynomials of degree at least three. Symmetric stress approximations of…
Multilevel methods represent a powerful approach in numerical solution of partial differential equations. The multilevel structure can also be used to construct estimates for total and algebraic errors of computed approximations. This paper…
We consider a conforming finite element approximation of the Reissner-Mindlin system. We propose a new robust a posteriori error estimator based on H(div) conforming finite elements and equilibrated fluxes. It is shown that this estimator…
In this paper, a posteriori error estimates of functional type for a stationary diffusion problem with nonsymmetric coefficients are derived. The estimate is guaranteed and does not depend on any particular numerical method. An algorithm…
The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate…
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple…