Related papers: An adaptive finite element PML method for the elas…
In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for…
In the author's previous paper (Zhang et al. 2022), exponential convergence was proved for the perfectly matched layers (PML) approximation of scattering problems with periodic surfaces in 2D. However, due to the overlapping of…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
We present a locally adapted parametric finite element method for interface problems. For this adapted finite element method we show optimal convergence for elliptic interface problems with a discontinuous diffusion parameter. The method is…
The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…
Perfectly Matched Layer (PML) is a widely adopted non-reflecting boundary treatment for wave simulations. Reducing numerical reflections from a discretized PML has been a long lasting challenge. This paper presents a new discrete PML for…
This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress…
We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direct extension of the finite element…
We design a primal-dual stabilized finite element method for the numerical approximation of a data assimilation problem subject to the acoustic wave equation. For the forward problem, piecewise affine, continuous, finite element functions…
The perfectly matched layer (PML) formulation is a prominent way of handling radiation problems in unbounded domain and has gained interest due to its simple implementation in finite element codes. However, its simplicity can be advanced…
In this paper, we design a truly exact and optimal perfect absorbing layer (PAL) for domain truncation of the two-dimensional Helmholtz equation in an unbounded domain with bounded scatterers. This technique is based on a complex…
We prove stability and exponential convergence of the Perfectly Matched Layer (PML) method for acoustic scattering on manifolds with axial analytic quasicylindrical ends. These manifolds model long-range geometric perturbations (e.g.…
In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…
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…
It is known that any {\em real coordinate transformation} (RCT) to compress waves in an unbounded domain into a bounded domain results in infinite oscillations that cannot be resolved by any grid-based method. In this paper, we intend to…
The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or…
We summarise three applications of the obstacle problem to membrane contact, elastoplastic torsion and cavitation modelling, and show how the resulting models can be solved using mixed finite elements. It is challenging to construct fixed…
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…
This article takes the form of a tutorial on the use of a particular class of mixed finite element methods, which can be thought of as the finite element extension of the C-grid staggered finite difference method. The class is often…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…