Related papers: Dual Formulations of Mixed Finite Element Methods …
Mixed-dimensional partial differential equations arise in several physical applications, wherein parts of the domain have extreme aspect ratios. In this case, it is often appealing to model these features as lower-dimensional manifolds…
The EHP and the MCAP provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. Both approaches utilize the mixed formulation and lead to the development of…
The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has…
In this paper, we propose and analyze a mixed virtual element method for the approximation of the eigenvalues and eigenfunctions of the two-dimensional elasticity eigenvalue problem. Under standard assumptions on polygonal meshes, we prove…
We consider fourth order singularly perturbed boundary value problems with two small parameters, and the approximation of their solution by the $hp$ version of the Finite Element Method on the {\emph{Spectral Boundary Layer}} mesh from…
Given a sequence of finite element spaces which form a de Rham sequence, we will construct a dual representation of these spaces with associated differential operators which connect these spaces such that they also form a de Rham sequence.…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
The simulation of fluid flow problems, specifically incompressible flows governed by the Navier-Stokes equations (NSE), holds fundamental significance in a range of scientific and engineering applications. Traditional numerical methods…
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
We hybridize the methods of finite element exterior calculus for the Hodge-Laplace problem on differential $k$-forms in $\mathbb{R}^n$. In the cases $k = 0$ and $k = n$, we recover well-known primal and mixed hybrid methods for the scalar…
A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…
In this paper, we develop the numerical theory of decoupled modified characteristic finite element method with different subdomain time steps for the mixed stabilized formulation of nonstationary dual-porosity-Navier-Stokes model. Based on…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…
This paper develops divergence-free mixed finite element methods for the Stokes equation. Using H(div)-conforming velocities and discontinuous pressures ensures the inf-sup condition for the velocity--pressure pair and yields pointwise…
In the first part of planned series of papers the formal general solutions to selection of 80 examples of different types of second order nonlinear PDEs in two independent variables with constant parameters are given. The main goal here is…
We present a multiscale finite element method for a diffusion problem with rough and high contrast coefficients. The construction of the multiscale finite element space is based on the localized orthogonal decomposition methodology and it…
We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimentional case in certain discrete…
The dual continuum model serves as a powerful tool in the modeling of subsurface applications. It allows a systematic coupling of various components of the solutions. The system is of multiscale nature as it involves high heterogeneous and…
The flux-mortar mixed finite element method was recently developed for a general class of domain decomposition saddle point problems on non-matching grids. In this work we develop the method for Darcy flow using the multipoint flux…
Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…