Related papers: Biot model with generalized eigenvalue problems fo…
Efficient and suitably preconditioned iterative solvers for elliptic partial differential equations (PDEs) of the convection-diffusion type are used in all fields of science and engineering. To achieve optimal performance, solvers have to…
In the context of isogeometric analysis, we consider two discretization approaches that make the resulting stiffness matrix nonsymmetric even if the differential operator is self-adjoint. These are the collocation method and the…
We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporating stabilization terms. Unlike…
This paper presents and analyzes a parallelizable iterative procedure based on domain decomposition for primal-dual weak Galerkin (PDWG) finite element methods applied to the Poisson equation. The existence and uniqueness of the PDWG…
This work extends the concepts of algebraic flux correction and convex limiting to continuous high-order Bernstein finite element discretizations of scalar hyperbolic problems. Using an array of adjustable diffusive fluxes, the standard…
We derive a new parallel-in-time approach for solving large-scale optimization problems constrained by time-dependent partial differential equations arising from fluid dynamics. The solver involves the use of a block circulant approximation…
We propose and rigorously analyse semi- and fully discrete discontinuous Galerkin methods for an initial and boundary value problem describing inertial viscoelasticity in terms of elastic and viscoelastic stress components, and with mixed…
We analyze a quasi-static Biot system of poroelasticity for both compressible and incompressible constituents. The main feature of this model is a nonlinear coupling of pressure and dilation through the system's permeability tensor. Such a…
The balancing domain decomposition methods (BDDC) are originally introduced for symmetric positive definite systems and have been extended to the nonsymmetric positive definite system from the linear finite element discretization of…
We present a new approach and an algorithm for optimizing the material configuration and behaviour of a fluid saturated porous medium in a two-scale setting. The state problem is governed by the Biot model describing the fluid-structure…
Linear systems with large differences between coefficients ("discontinuous coefficients") arise in many cases in which partial differential equations(PDEs) model physical phenomena involving heterogeneous media. The standard approach to…
In this work, we consider the popular P1-RT0-P0 discretization of the three-field formulation of Biot's consolidation problem. Since this finite-element formulation does not satisfy an inf-sup condition uniformly with respect to the…
We present a new line-based discontinuous Galerkin (DG) discretization scheme for first- and second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements,…
In this paper, we develop monolithic limiting techniques for enforcing nonlinear stability constraints in enriched Galerkin (EG) discretizations of nonlinear scalar hyperbolic equations. To achieve local mass conservation and gain control…
We consider a stable unique continuation problem for the wave equation where the initial data is lacking and the solution is reconstructed using measurements in some subset of the bulk domain. Typically fairly sophisticated space-time…
We introduce a family of mixed methods and discontinuous Galerkin discretisations designed to numerically solve the Oseen equations written in terms of velocity, vorticity, and Bernoulli pressure. The unique solvability of the continuous…
We consider fully discrete finite element approximations for a semilinear optimal control system of partial differential equations in two cases: for distributed and Robin boundary control. The ecological predator-prey optimal control model…
The fixed-stress splitting scheme is a popular method for iteratively solving the Biot equations. The method successively solves the flow and mechanic subproblems while adding a stabilizing term to the flow equation, which includes a…
We study two-stage stochastic optimization models with mixed-integer decision variables appearing in both stages. For these models, dual decomposition enables parallel computing implementation and can quickly provide a lower bound for the…
In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider the fixed-stress splitting scheme, which is a popular method for iteratively solving Biot's equations. It is well-known…