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The purpose of this article is to approximately compute the eigenvalues of the symmetric Dirichlet Laplacian within an interval $(0,\Lambda)$. A novel domain decomposition Ritz method, partition of unity condensed pole interpolation, is proposed. This ...

This work introduces a computational framework for applying absolute electrical impedance tomography to head imaging without accurate information on the head shape or the electrode positions. A library of 50 heads is employed to build a principal ...

Efficient solution of the lowest eigenmodes is studied for a family of related eigenvalue problems with common $2\times 2$ block structure. It is assumed that the upper diagonal block varies between different versions while the lower diagonal block and the ...

Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating the distribution of optical parameters inside tissues from photoacoustic images, which are formed by combining optical information and ultrasonic propagation. This ...

The finite element method usually requires regular or strongly regular families of partitions in order to get guaranteed a priori or a posteriori error estimates. In this paper we examine the recently invented longest-edge bisection algorithm that ...

This work considers the Cauchy problem for a second order elliptic operator in a bounded domain. A new quasi-reversibility approach is introduced for approximating the solution of the ill-posed Cauchy problem in a regularized manner. The method is based on a ...

In this paper, we study the convergence of a two-level preconditioned GMRES for linear systems related to first order finite element discretizations of Helmholtz equation in a lossy media. Due to losses, the finite element system matrix is nonnormal. To ...

In this paper, a unified framework for a posteriori error estimation for the Stokes problem is developed. It is based on $$[H^1_0(\Omega )]^d$$ -conforming velocity reconstruction and $$\underline{\boldsymbol{H}}(\mathrm{div},\Omega )$$ -conforming, locally conservative flux (stress) reconstruction. It gives guaranteed, fully ...

In this note, we show how to apply preconditioners designed for piecewise linear finite element discretizations of the Poisson problem as preconditioners for the mixed problem. Our preconditioner can be applied both to the original and to the ...

We show that the famous maximum angle condition in the finite element analysis is not necessary to achieve the optimal convergence rate when simplicial finite elements are used to solve elliptic problems. This condition is only sufficient. In fact, ...

We examine a generalized conforming bisection (GCB-)algorithm which allows both global and local nested refinements of the triangulations without generating hanging nodes. It is based on the notion of a mesh density function which prescribes where and ...

In this paper we analyze the discrete maximum principle (DMP) for a non-stationary diffusion-reaction problem solved by means of prismatic finite elements and @q-method. We derive geometric conditions on the shape parameters of prismatic partitions and ...

First we introduce a mesh density function that is used to define a criterion to decide, where a simplicial mesh should be fine (dense) and where it should be coarse Further, we propose a new bisection algorithm that chooses for bisection an edge in a ...

In this paper we analyse the discrete maximum principle (DMP) for a stationary diffusion-reaction problem solved by means of prismatic finite elements. We derive geometric conditions on the shape parameters of the prismatic partitions which guarantee ...

In this work we discuss weakening requirements on the set of sufficient conditions due to Ph. Ciarlet [4,5] for matrices associated to linear finite element schemes, which is commonly used for proving validity of discrete maximum principles (DMPs) for ...

A new a posteriori error estimate is derived for the stationary convection-reaction-diffusion equation. In order to estimate the approximation error in the usual energy norm, the underlying bilinear form is decomposed into a computable integral and two ...