Difference potentials method for the nonlinear convection-diffusion equation with interfaces

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Elliptic equations and elliptic systems (35Jxx)

Cites Work

A consistent immersed finite element method for the interface elasticity problems
High-order numerical schemes based on difference potentials for 2D elliptic problems with material interfaces
Weak Galerkin methods for second order elliptic interface problems
High order numerical simulation of the transmission and scattering of waves using the method of difference potentials
IIM-based ADI finite difference scheme for nonlinear convection-diffusion equations with interfaces
A dimension by dimension splitting immersed interface method for heat conduction equation with interfaces
Numerical solutions of two-dimensional Burgers' equations by discrete Adomian decomposition method
Optimal convergence analysis of an immersed interface finite element method
Finite element methods and their convergence for elliptic and parabolic interface problems
Numerical solution of the wave equation with variable wave speed on nonconforming domains by high-order difference potentials
The immersed interface method for a nonlinear chemical diffusion equation with local sites of reactions
A method of boundary equations for unsteady hyperbolic problems in 3D
High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
The method of difference potentials for the Helmholtz equation using compact high order schemes
Upwind-difference potentials method for Patlak-Keller-Segel chemotaxis model
High-order finite element methods for interface problems: theory and implementations
An implicit finite difference scheme for the numerical solutions of two-dimensional Burgers equations
Parameter uniform optimal order numerical approximations for time-delayed parabolic convection diffusion problems involving two small parameters
Solving the Helmholtz equation for general smooth geometry using simple grids
Difference potentials method for models with dynamic boundary conditions and bulk-surface problems
Method of difference potentials for evolution equations with lacunas
A novel PDE based image restoration: Convection-diffusion equation for image denoising
Efficient numerical algorithms based on difference potentials for chemotaxis systems in 3D
Professor V. S. Ryaben'kii. On the occasion of the 90-th birthday
High-order difference potentials methods for 1D elliptic type models
High-order accurate difference potentials methods for parabolic problems
Matched interface and boundary method for elasticity interface problems
High-order numerical solution of the Helmholtz equation for domains with reentrant corners
Numerical solutions of the modified Burgers' equation by finite difference methods
High-order accurate methods based on difference potentials for 2D parabolic interface models
Heat transfer to a draining film
On the accuracy of finite element approximations to a class of interface problems
On the Solution of the Elliptic Interface Problems by Difference Potentials Method
A High-Order Numerical Method for the Helmholtz Equation with Nonstandard Boundary Conditions
Novel fitted operator finite difference methods for singularly perturbed elliptic convection–diffusion problems in two dimensions
An Immersed Interface Technique for the Numerical Solution of the Heat Equation on a Moving Domain
A uniformly convergent alternating direction HODIE finite difference scheme for 2D time-dependent convection-diffusion problems
Difference potentials analogous to Cauchy integrals
The Immersed Interface/Multigrid Methods for Interface Problems
Analysis of the L1 scheme for a time fractional parabolic–elliptic problem involving weak singularity
Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem
A new stable finite difference scheme and its error analysis for two‐dimensional singularly perturbed convection–diffusion equations
A higher order hybrid-numerical approximation for a class of singularly perturbed two-dimensional convection-diffusion elliptic problem with non-smooth convection and source terms
Numerical treatment of a singularly perturbed 2-D convection-diffusion elliptic problem with Robin-type boundary conditions
A second order fractional step hybrid numerical algorithm for time delayed singularly perturbed 2D convection-diffusion problems
Algorithm composition scheme for problems in composite domains based on the difference potential method
Weighted variable based numerical scheme for time-lagged semilinear parabolic problems including small parameter
A computational method for a two-parameter singularly perturbed elliptic problem with boundary and interior layers
A novel numerical technique for solving time fractional nonlinear diffusion equations involving weak singularities
A finite difference method for a singularly perturbed 2‐D elliptic convection‐diffusion PDEs on Shishkin‐type meshes with non‐smooth convection and source terms
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