Related papers: A Compatible Finite Element Discretisation for the…
In this paper, we consider a class of systems of nonlinear equations, which arise in discretized mixed formulations of problems in solid mechanics by $hp$-finite elements. We introduce a semismooth Newton solver for this specific class and…
In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After stating unique solvability of the resulting semi-discrete problem,…
Within this paper, we introduce partially and fully decoupled time stepping schemes for linear thermo-poroelasticity. This means that the mechanics, heat, and flow equations can be solved sequentially. We provide sufficient conditions on…
This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…
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,…
Biot's consolidation model in poroelasticity has a number of applications in science, medicine, and engineering. The model depends on various parameters, and in practical applications these parameters ranges over several orders of…
We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
The accurate and efficient representation of atmospheric dynamics remains a central challenge in numerical weather prediction. A particular difficulty arises from the strong anisotropy of the atmosphere, in which horizontal and vertical…
The paper develops a solver based on a conforming finite element method for a 3D--1D coupled incompressible flow problem. New coupling conditions are introduced to ensure a suitable bound for the cumulative energy of the model. We study the…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
We introduce a new discretization of a mixed formulation of the incompressible Stokes equations that includes symmetric viscous stresses. The method is built upon a mass conserving mixed formulation that we recently studied. The improvement…
We consider data assimilation for the heat equation using a finite element space semi-discretization. The approach is optimization based, but the design of regularization operators and parameters rely on techniques from the theory of…
In this work, we propose a structure-preserving discretisation for the recently studied Cahn-Hilliard-Biot system using conforming finite elements in space and problem-adapted explicit-implicit Euler time integration. We prove that the…
The parameters in the governing system of partial differential equations of multicompartmental poroelastic models typically vary over several orders of magnitude making its stable discretization and efficient solution a challenging task. In…
In this work a non-conservative balance law formulation is considered that encompasses the rotating, compressible Euler equations for dry atmospheric flows. We develop a semi-discretely entropy stable discontinuous Galerkin method on…
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…
We analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the…
This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…