Related papers: Dual Formulations of Mixed Finite Element Methods …
This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is assumed to…
We develop the theory of mixed finite elements in terms of special inverse systems of complexes of differential forms, defined over cellular complexes. Inclusion of cells corresponds to pullback of forms. The theory covers for instance…
In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous…
With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent…
Pendry and MacKinnon meaningful discretization of Maxwell's equations was put forward specifically as part of a finite-element numerical algorithm. By contrast with a numerical approach, in the same spirit evoked by the relationships…
A discretization method with non-matching grids is proposed for the coupled Stokes-Darcy problem that uses a mortar variable at the interface to couple the marker and cell (MAC) method in the Stokes domain with the Raviart-Thomas mixed…
Finite element exterior calculus (FEEC) has been developed as a systematical framework for constructing and analyzing stable and accurate numerical method for partial differential equations by employing differential complexes. This paper is…
We define signed dual volumes at all dimensions for circumcentric dual meshes. We show that for pairwise Delaunay triangulations with mild boundary assumptions these signed dual volumes are positive. This allows the use of such Delaunay…
We present a local formulation for 2D Discrete Exterior Calculus (DEC) similar to that of the Finite Element Method (FEM), which allows a natural treatment of material heterogeneity (element by element). It also allows us to deduce, in a…
A short proof of convergence for the discretization of the Hodge-Dirac operator in the framework of discrete exterior calculus (DEC) is provided using the techniques established in [Johnny Guzm\'an and Pratyush Potu, A Framework for…
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…
Unconditionally stable finite element methods for Darcy flow are derived by adding least-squares residual forms of the governing equations to the classical mixed formulations. The proposed methods are free of mesh dependent stabilization…
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of…
In this paper we introduce a new class of finite element discretizations of the quadratic optimal transport problem based on its dynamical formulation. These generalize to the finite element setting the finite difference scheme proposed by…
Numerical methods: mimetic finite differences and finite elements, are analyzed from a numerical point of view. It seeks to conclude on the efficiency, order of convergence and computational cost of these methods. The analysis is done in…
This paper introduces an approach to decoupling singularly perturbed boundary value problems for fourth-order ordinary differential equations that feature a small positive parameter $\epsilon$ multiplying the highest derivative. We…
We propose a new mixed finite element method for the three-dimensional steady magnetohydrodynamic (MHD) kinematics equations for which the velocity of the fluid is given. Although prescribing the velocity field leads to a simpler model than…
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…