Error control and adaptivity for a phase relaxation model
Error Control and Andaptivity for a Phase Relaxation Model
The phase relaxation model is a diffuse interface model with small parameter ε which consists of a parabolic PDE for temperature θ and an ODE with double obstacles for phase variable χ. To decouple the system a semi-explicit Euler method with variable step-size τ is used for time discretization, which requires the stability constraint τ ≤ ε. Conforming piecewise linear finite elements over highly graded simplicial meshes with parameter h are further employed for space discretization. A posteriori...
Error estimate for a fully discrete spectral scheme for Korteweg-de Vries-Kawahara equation
We are concerned with convergence of spectral method for the numerical solution of the initial-boundary value problem associated to the Korteweg-de Vries-Kawahara equation (Kawahara equation, in short), which is a transport equation perturbed by dispersive terms of the 3rd and 5th order. This equation appears in several fluid dynamics problems. It describes the evolution of small but finite amplitude long waves in various problems in fluid dynamics. These equations are discretized in space by the...
Error estimate for the characteristic method involving Oldroyd derivative in a tensorial transport problem.
Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the -space
The Rothe-Galerkin method is used for discretization. The rate of convergence in for the approximate solution of a quasilinear parabolic equation with a Volterra operator on the right-hand side is established.
Error estimates and step-size control for the approximate solution of a first order evolution equation
Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system
Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present. Various physical parameters appearing in the...
Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system
Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present....
Error Estimates for a Galerkin Method for a Class of Model Equations for Long Waves.
Error estimates for barycentric finite volumes combined with nonconforming finite elements applied to nonlinear convection-diffusion problems
The subject of the paper is the derivation of error estimates for the combined finite volume-finite element method used for the numerical solution of nonstationary nonlinear convection-diffusion problems. Here we analyze the combination of barycentric finite volumes associated with sides of triangulation with the piecewise linear nonconforming Crouzeix-Raviart finite elements. Under some assumptions on the regularity of the exact solution, the and error estimates are established. At the end...
Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method
The identification problem of a functional coefficient in a parabolic equation is considered. For this purpose an output least squares method is introduced, and estimates of the rate of convergence for the Crank-Nicolson time discretization scheme are proved, the equation being approximated with the finite element Galerkin method with respect to space variables.
Error estimates for Euler forward scheme related to two-phase Stefan problems
Error estimates for finite volume scheme for Perona--Malik equation.
Error Estimates for Galerkin Methods for Quasilinear Parabolic and Elliptic Differential Equations in Divergence Form.
Error estimates for Galerkin reduced-order models of the semi-discrete wave equation
Galerkin reduced-order models for the semi-discrete wave equation, that preserve the second-order structure, are studied. Error bounds for the full state variables are derived in the continuous setting (when the whole trajectory is known) and in the discrete setting when the Newmark average-acceleration scheme is used on the second-order semi-discrete equation. When the approximating subspace is constructed using the proper orthogonal decomposition, the error estimates are proportional to the sums...
Error estimates for nonlinear convective problems in the finite element method
We describe the basic ideas needed to obtain apriori error estimates for a nonlinear convection diffusion equation discretized by higher order conforming finite elements. For simplicity of presentation, we derive the key estimates under simplified assumptions, e.g. Dirichlet-only boundary conditions. The resulting error estimate is obtained using continuous mathematical induction for the space semi-discrete scheme.
Error estimates for scalar conservation laws by a kinetic approach.
Error estimates for the semidiscrete finite element approximation of linear nonlocal parabolic equations.
Error estimates of a difference approximation method for a backward heat conduction problem.
Error estimates of a fully discrete linear approximation scheme for Stefan problem.