Related papers: Compatible finite element methods for numerical we…
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…
In this paper, finite element method is applied to Leland's model for numerical simulation of option pricing with transaction costs. Spatial finite element models based on P1 and/or P2 elements are formulated in combination with a…
We discuss algorithms applicable to the numerical solution of second-order ordinary differential equations by finite-differences. We make particular reference to the solution of the dissipative particle dynamics fluid model, and present…
We analyze the application to elastodynamic problems of mixed finite element methods for elasticity with weak symmetry. Our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without…
We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection…
A finite element model and its equivalent electronic analogue circuit of hydraulic transmission lines have been developed. Basic equations are approximated to be a set of ordinary differential equations that can be represented in state…
A mixed finite element method for the Navier-Stokes equations is introduced in which the stress is a primary variable. The variational formulation retains the mathematical structure of the Navier-Stokes equations and the classical theory…
We provide an approach to implementing the shallow atmosphere approximation in three dimensional finite element discretisations for dynamical cores. The approach makes use of the fact that the shallow atmosphere approximation metric can be…
We introduce a pressure robust Finite Element Method for the linearized Magnetohydrodynamics equations in three space dimensions, which is provably quasi-robust also in the presence of high fluid and magnetic Reynolds numbers. The proposed…
A vertical slice model is developed for the Euler-Boussinesq equations with a constant temperature gradient in the direction normal to the slice (the Eady-Boussinesq model). The model is a solution of the full three-dimensional equations…
There are very few results on mixed finite element methods on surfaces. A theory for the study of such methods was given recently by Holst and Stern, using a variational crimes framework in the context of finite element exterior calculus.…
In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…
In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…
A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of…
Staggered grid finite difference scheme is widely used for the first order elastic wave equation, which constitutes the basis for least-squares reverse time migration and full waveform inversion. It is of great importance to improve the…
In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…
We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
Within the framework of finite element systems, we show how spaces of differential forms may be constructed, in such a way that they are equipped with commuting interpolators and contain prescribed functions, and are minimal under these…
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…