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A singularly perturbed parabolic problem of convection-diffusion type with incompatible inflow boundary and initial conditions is examined. In the case of constant coefficients, a set of singular functions are identified which match certain…

Numerical Analysis · Mathematics 2022-12-20 Jose Luis Gracia , Eugene O'Riordan

In this paper we analyze the error as well for the semi-discretization as the full discretization of a time-dependent convection-diffusion problem. We use for the discretization in space the local discontinuous Galerkin (LDG) method on a…

Numerical Analysis · Mathematics 2020-12-08 Yao Cheng , Yanjie Mei , Hans-Goerg Roos

We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…

Analysis of PDEs · Mathematics 2017-05-31 Clément Cancès , Claire Chainais-Hillairet , Stella Krell

We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted piecewise…

Numerical Analysis · Mathematics 2017-09-29 Simon Becher

This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…

Probability · Mathematics 2015-09-21 Achref Bachouch , Mohamed Anis Ben Lasmar , Anis Matoussi , Mohamed Mnif

This paper introduces an approach to decoupling singularly perturbed boundary value problems for fourth-order ordinary differential equations that feature a small positive parameter $\epsilon$ multiplying the highest derivative. We…

Numerical Analysis · Mathematics 2023-06-13 Charuka D. Wickramasinghe

Numerical approximations to the solution of a linear singularly perturbed parabolic reaction-diffusion problem with incompatible bound\-ary-initial data are generated, The method involves combining the computational solution of a classical…

Numerical Analysis · Mathematics 2018-11-19 Jose Luis Gracia , Eugene O'Riordan

A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…

Numerical Analysis · Mathematics 2009-06-23 M. Paramasivam , S. Valarmathi , J. J. H. Miller

A system of singularly perturbed ordinary differential equations of first order with given initial conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These parameters are assumed to be…

Numerical Analysis · Mathematics 2009-03-11 S Valarmathi , John J H Miller

We consider an optimal control problem on a bounded domain $\Omega\subset\mathbb{R}^2,$ governed by a parabolic convection--diffusion--reaction equation with pointwise control constraints. We follow the optimize--then--discretize approach,…

Numerical Analysis · Mathematics 2025-12-11 Christos Pervolianakis

In this paper, a class of linear parabolic systems of singularly perturbed second order differential equations of reaction-diffusion type with initial and Robin boundary conditions is considered. The components of the solution $\vec u$ of…

Numerical Analysis · Mathematics 2019-06-21 R. Ishwariya , J. J. H. Miller , S. Valarmathi

A numerical method is formulated for the solution of the advective Cahn-Hilliard (CH) equation with constant and degenerate mobility in three-dimensional porous media with non-vanishing velocity on the exterior boundary. The CH equation…

Numerical Analysis · Mathematics 2016-10-12 Florian Frank , Chen Liu , Faruk O. Alpak , Beatrice Riviere

In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…

Numerical Analysis · Mathematics 2020-05-06 Daijun Jiang , Yikan Liu , Dongling Wang

This work addresses an inverse reconstruction task for a time-fractional pseudo-parabolic model with a temporally varying coefficient. By imposing Dirichlet boundary conditions, we aim to recover the unknown initial state from observations…

Numerical Analysis · Mathematics 2026-03-17 Arshyn Altybay

A singularly perturbed problem involving two singular perturbation parameters is discretized using the classical upwinded finite difference scheme on an appropriate piecewise-uniform Shishkin mesh. Scaled discrete derivatives (with scaling…

Numerical Analysis · Mathematics 2017-08-03 Eugene O'Riordan , Maria Pickett

In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting…

Numerical Analysis · Mathematics 2024-05-20 Bangti Jin , Xiliang Lu , Qimeng Quan , Zhi Zhou

A singularly perturbed convection-diffusion problem posed on the unit square in $\mathbb{R}^2$, whose solution has exponential boundary layers, is solved numerically using the local discontinuous Galerkin (LDG) method with piecewise…

Numerical Analysis · Mathematics 2022-06-20 Yao Cheng , Shan Jiang , Martin Stynes

Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…

Numerical Analysis · Mathematics 2021-01-25 Andrea Barth , Andreas Stein

In this article, we study the unique determination of convection term and the time-dependent density coefficient appearing in a convection-diffusion equation from partial Dirichlet to Neumann map measured on boundary.

Analysis of PDEs · Mathematics 2019-11-14 Suman Kumar Sahoo , Manmohan Vashisth

In this article, we consider discrete schemes for a fractional diffusion equation involving a tempered fractional derivative in time. We present a semi-discrete scheme by using the local discontinuous Galerkin (LDG) discretization in the…

Numerical Analysis · Mathematics 2017-04-27 Xiaorui Sun , Fengfqun Zhao , Can Li