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We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete…
This paper is concerned with the partitioned iterative formulation to simulate the fluid-structure interaction of a nonlinear multibody system in an incompressible turbulent flow. The proposed formulation relies on a three-dimensional (3D)…
Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite element method and mortar methods. Our…
We analyze Galerkin discretizations of a new well-posed mixed space-time variational formulation of parabolic PDEs. For suitable pairs of finite element trial spaces, the resulting Galerkin operators are shown to be uniformly stable. The…
A Galerkin finite element method for the membrane elasticity problem on a meshed surface is constructed by using two-dimensional elements extended into three dimensions. The membrane finite element model is established using the intrinsic…
In the framework of a mixed finite element method, a structure-preserving formulation for incompressible magnetohydrodynamic (MHD) equations with general boundary conditions is proposed. A leapfrog-type temporal scheme fully decouples the…
We prove linear convergence for a new family of modified Dirichlet--Neumann methods applied to quasilinear parabolic equations, as well as the convergence of the Robin--Robin method. Such nonoverlapping domain decomposition methods are…
The direct numerical simulation of metal additive manufacturing processes such as laser powder bed fusion is challenging due to the vast differences in spatial and temporal scales. Classical approaches based on locally refined finite…
We present a scalable 2D Galerkin spectral element method solution to the linearized potential flow radiation problem for wave induced forcing of a floating offshore structure. The pseudo-impulsive formulation of the problem is solved in…
In this paper, we develop the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) in mixed formulation applied to parabolic equations with heterogeneous diffusion coefficients. The construction of the…
In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods (MFEM) in space for simulating…
We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…
Hybrid finite element methods such as hybridizable discontinuous Galerkin, hybrid high-order and weak Galerkin have emerged as powerful techniques for solving partial differential equations on general polytopal meshes. Despite their diverse…
We introduce a new mixed discontinuous/continuous Galerkin finite element for solving the 2- and 3-dimensional wave equations and equations of incompressible flow. The element, which we refer to as P1dg-P2, uses discontinuous piecewise…
We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…
This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical M\"uller equation to composite structures through the global multi-trace…
Pseudo-parabolic equations have been used to model unsaturated fluid flow in porous media. In this paper it is shown how a pseudo-parabolic equation can be upscaled when using a spatio-temporal decomposition employed in the…
In this paper, we consider a parabolic problem with time-dependent heterogeneous coefficients. Many applied problems have coupled space and time heterogeneities. Their homogenization or upscaling requires cell problems that are formulated…
We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…