Related papers: Adaptive boundary element methods for the computat…
We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are…
We present an efficient and robust semi-analytical formulation to compute the electric potential due to arbitrary-located point electrodes in three-dimensional cylindrically stratified media, where the radial thickness and the medium…
We consider the Galerkin boundary element method (BEM) for weakly-singular integral equations of the first-kind in 2D. We analyze some residual-type a posteriori error estimator which provides a lower as well as an upper bound for the…
A parabolic free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which is hinged at its boundary, the plates being held at…
A binary three-dimensional (3D) image $I$ is well-composed if the boundary surface of its continuous analog is a 2D manifold. Since 3D images are not often well-composed, there are several voxel-based methods ("repairing" algorithms) for…
Consider the electromagnetic scattering of a time-harmonic plane wave by an open cavity which is embedded in a perfectly electrically conducting infinite ground plane. This paper is concerned with the numerical solutions of the transverse…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
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 $d\geq 1$ dimensions. Our main approach consists of…
An effective quantum number determining with high accuracy the levels ordering in arbitrary centrally symmetric potentials for any space dimensionality is introduced and calculated by means of certain universal methods based on the known…
Outside the core of the plasma, the plasma current and pressure rapidly transition to zero in a scrape-off or edge region or plasma-vacuum interface. However, existing tools for fixed-boundary magnetohydrodynamic equilibria in 2D and 3D…
The Continuous p-Dispersion Problem (CpDP) with boundary constraints asks for the placement of a fixed number of points in a compact subset of Euclidean space such that the minimum distance between any two points, as well as the points and…
We derive energy-norm aposteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the first completely rigorous derivation of ZZ…
Adaptive multilevel finite element methods are developed and analyzed for certain elliptic systems arising in geometric analysis and general relativity. This class of nonlinear elliptic systems of tensor equations on manifolds is first…
We construct energy-dependent potentials for which the Schroedinger equations admit solu- tions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations…
This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
In recent years there have been tremendous advances in the theoretical understanding of boundary integral equations for Maxwell problems. In particular, stable dual pairing of discretisation spaces have been developed that allow robust…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
We present algorithms for computing weakly singular and near-singular integrals arising when solving the 3D Helmholtz equation with curved boundary elements. These are based on the computation of the preimage of the singularity in the…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…