Related papers: Mass-conservative and positivity preserving second…
The problem of recovering partial derivatives of high orders of bivariate functions with finite smoothness is studied. Based on the truncation method, a numerical differentiation algorithm was constructed, which is optimal by the order,…
In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…
In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite…
In this work, we present a positivity-preserving adaptive filtering approach for discontinuous spectral element approximations of the ideal magnetohydrodynamics equations. This approach combines the entropy filtering method (Dzanic and…
We study spatially semidiscrete and fully discrete finite volume element methods for the homogeneous heat equation with homogeneous Dirichlet boundary conditions and derive error estimates for smooth and nonsmooth initial data. We show that…
Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…
The problems of optimal recovery of unbounded operators are studied. Optimality means the highest possible accuracy and the minimal amount of discrete information involved. It is established that the truncation method, when certain…
We introduce a novel positivity-preserving, parameter-free numerical stabilisation approach for high-order discontinuous spectral element approximations of compressible multi-species flows. The underlying stabilisation method is the…
The paper introduces a new way to construct dissipative solutions to a second order variational wave equation. By a variable transformation, from the nonlinear PDE one obtains a semilinear hyperbolic system with sources. In contrast with…
We clarify how close a second order fully nonlinear equation can come to uniform ellipticity, through counting large eigenvalues of the linearized operator. This suggests an effective and novel way to understand the structure of fully…
We present a new formulation of the Einstein equations that casts them in an explicitly first order, flux-conservative, hyperbolic form. We show that this now can be done for a wide class of time slicing conditions, including maximal…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and…
This article is about a problem in the numerical analysis of random operators. We study a version of the finite section method for the approximate solution of equations $Ax=b$ in infinitely many variables, where $A$ is a random Jacobi…
We construct a new compact semi-explicit three-level in time fourth-order finite-difference scheme for numerical solving the general multidimensional acoustic wave equation, where both the speed of sound and density of a medium are…
A systematic numerical study on weak Galerkin (WG) finite element method for second order linear parabolic problems is presented by allowing polynomial approximations with various degrees for each local element. Convergence of both…
We formulate a well-posedness and approximation theory for a class of generalised saddle point problems with a specific form of constraints. In this way we develop an approach to a class of fourth order elliptic partial differential…
We introduce a new dynamical system, at the interface between second-order dynamics with inertia and Newton's method. This system extends the class of inertial Newton-like dynamics by featuring a time-dependent parameter in front of the…
We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represent each conservation law or dissipation inequality by means…
We introduce a (linear) positive and asymptotic preserving method or solving the one-group radiation transport equation. The approximation in space is discretization agnostic: the space approximation can be done with continuous or…