Robust error estimates in weak norms for advection dominated transport problems with rough data [PDF]
, 2014 We consider mixing problems in the form of transient convection--diffusion equations with a velocity vector field with multiscale character and rough data.
Burman, Erik
core +2 more sources
Galerkin and Runge–Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence [PDF]
, 2011 . We unify the formulation and analysis of Galerkin and Runge–Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximate solutions, allows us to establish a posteriori ...
A. Lozinski +21 more
core +5 more sources
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.This paper presents a class of singularly perturbed parabolic‐type reaction diffusion problems. Due to the presence of a small parameter ε, (0 < ε ≪ 1) as a diffusion coefficient, the proposed problem exhibits twin boundary layers in the neighborhood of the end points of the spatial domain near x = 0 and x = 1.
Amare Worku Demsie +3 more
wiley +1 more source
Linear-implicit strong schemes for Itô-Galkerin approximations of stochastic PDEs [PDF]
, 2010 Linear-implicit versions of strong Taylor numerical schemes for finite dimensional Itô stochastic differential equations (SDEs) are shown to have the same order as the original scheme.
Kloeden, Peter E., Shott, Stephen
core
A Posteriori Error Estimation for the p-curl Problem
, 2020 We derive a posteriori error estimates for a semi-discrete finite element approximation of a nonlinear eddy current problem arising from applied superconductivity, known as the $p$-curl problem. In particular, we show the reliability for non-conforming N\
Laforest, Marc, Wan, Andy T. S.
core +1 more source
Interior a posteriori error estimates for time discrete approximations of parabolic problems [PDF]
, 2012 a posteriori error estimates for time discrete approximations ...
Charalambos Makridakis +3 more
core +1 more source
Error analysis of a continuous-discontinuous Galerkin finite element method for generalized 2D vorticity dynamics [PDF]
, 2005 A detailed a priori error estimate is provided for a continuous-discontinuous Galerkin finite element method suitable for two-dimensional geophysical flows.
Bokhove, O. +2 more
core +1 more source
Time-stepping error bounds for fractional diffusion problems with non-smooth initial data
, 2014 We apply the piecewise constant, discontinuous Galerkin method to discretize a fractional diffusion equation with respect to time. Using Laplace transform techniques, we show that the method is first order accurate at the \$n\$th time level \$t_n\$, but ...
McLean, William, Mustapha, Kassem
core +1 more source
Numerical analysis of a non-clamped dynamic thermoviscoelastic contact problem
, 2019 In this work we analyze a non-clamped dynamic viscoelastic contact problem involving thermal effect. The friction law is described by a nonmonotone relation between the tangential stress and the tangential velocity.
Bartman, Piotr +3 more
core +1 more source
Unconditional stability of semi-implicit discretizations of singular flows
, 2017 A popular and efficient discretization of evolutions involving the singular $p$-Laplace operator is based on a factorization of the differential operator into a linear part which is treated implicitly and a regularized singular factor which is treated ...
Bartels, Sören +2 more
core +1 more source