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We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…
We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…
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…
Mixed dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimension. Such equations naturally arise in a wide range of scientific fields including geology,…
This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective…
This article investigates a space-time differential model related to the degradation of stone artifacts caused by exposure to air and atmospheric agents, which specifically lead to the accumulation of salt crystals in the material. A…
Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time…
In this work, we investigate the numerical reconstruction of inclusions in a semilinear elliptic equation arising in the mathematical modeling of cardiac ischemia. We propose an adaptive finite element method for the resulting constrained…
We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric elliptic problem. We prove the convergence and complexity of…
This paper explores how to adapt a new dynamical core to enable its use in one-way nested regional weather and climate models, where lateral boundary conditions (LBCs) are provided by a lower-resolution driving model. The dynamical core has…
The finite element method has become a preeminent simulation technique in electromagnetics. For problems involving anisotropic media and metamaterials, proper algorithms should be developed. It has been proved that discretizing in quadratic…
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…
This paper is devoted to the study of a novel mixed Finite Element Method for approximating the solutions of fourth order variational problems subjected to a constraint. The first problem we consider consists in establishing the convergence…
In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic…
In this paper, a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect…
We consider the numerical approximation of acoustic wave propagation problems by mixed BDM(k+1)-P(k) finite elements on unstructured meshes. Optimal convergence of the discrete velocity and super-convergence of the pressure by one order are…