Natalia Kopteva

Publication Activity (10 Years)

Years Active: 2001-2024
Publications (10 Years): 28

Top Topics

Error Estimates

Top Venues

SIAM J. Numer. Anal.

Numerische Mathematik

Publications

Sebastian Franz, Natalia Kopteva
On the solution existence for collocation discretizations of time-fractional subdiffusion equations. CoRR (2024)
Sebastian Franz, Natalia Kopteva
Time stepping adaptation for subdiffusion problems with non-smooth right-hand sides. CoRR (2024)
Sebastian Franz, Natalia Kopteva
On the Solution Existence for Collocation Discretizations of Time-Fractional Subdiffusion Equations. J. Sci. Comput. 100 (3) (2024)
Natalia Kopteva, Richard Rankin
Pointwise A Posteriori Error Estimates for Discontinuous Galerkin Methods for Singularly Perturbed Reaction-Diffusion Equations. SIAM J. Numer. Anal. 61 (4) (2023)
Sebastian Franz, Natalia Kopteva
Pointwise-in-time a posteriori error control for higher-order discretizations of time-fractional parabolic equations. J. Comput. Appl. Math. 427 (2023)
Alan Demlow, Sebastian Franz, Natalia Kopteva
Maximum norm a posteriori error estimates for convection-diffusion problems. CoRR (2022)
Natalia Kopteva, Martin Stynes
A posteriori error analysis for variable-coefficient multiterm time-fractional subdiffusion equations. CoRR (2022)
Natalia Kopteva
Maximum principle for time-fractional parabolic equations with a reaction coefficient of arbitrary sign. Appl. Math. Lett. 132 (2022)
Natalia Kopteva
Pointwise-in-time a posteriori error control for time-fractional parabolic equations. Appl. Math. Lett. 123 (2022)
Torsten Linß, Natalia Kopteva, Goran Radojev, Martin Ossadnik
A review of maximum-norm a posteriori error bounds for time-semidiscretisations of parabolic equations. CoRR (2022)
Sebastian Franz, Natalia Kopteva
Pointwise-in-time a posteriori error control for higher-order discretizations of time-fractional parabolic equations. CoRR (2022)
Sebastian Franz, Natalia Kopteva
Green's function estimates for a 2d singularly perturbed convection-diffusion problem: extended analysis. CoRR (2022)
Natalia Kopteva, Martin Stynes
A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations. J. Sci. Comput. 92 (2) (2022)
Natalia Kopteva
Error analysis of an L2-type method on graded meshes for a fractional-order parabolic problem. Math. Comput. 90 (327) (2021)
Natalia Kopteva
Pointwise-in-time a posteriori error control for time-fractional parabolic equations. CoRR (2021)
Natalia Kopteva
Lower a posteriori error estimates on anisotropic meshes. Numerische Mathematik 146 (1) (2020)
Natalia Kopteva
How accurate are finite elements on anisotropic triangulations in the maximum norm? J. Comput. Appl. Math. 364 (2020)
Natalia Kopteva, Xiangyun Meng
Error Analysis for a Fractional-Derivative Parabolic Problem on Quasi-Graded Meshes using Barrier Functions. SIAM J. Numer. Anal. 58 (2) (2020)
Natalia Kopteva
Error analysis for time-fractional semilinear parabolic equations using upper and lower solutions. CoRR (2020)
Natalia Kopteva
Error Analysis for Time-Fractional Semilinear Parabolic Equations Using Upper and Lower Solutions. SIAM J. Numer. Anal. 58 (4) (2020)
Natalia Kopteva
Logarithm cannot be removed in maximum norm error estimates for linear finite elements in 3D. Math. Comput. 88 (318) (2019)
Natalia Kopteva
Lower a posteriori error estimates on anisotropic meshes. CoRR (2019)
Natalia Kopteva
Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions. Math. Comput. 88 (319) (2019)
Elena Klimenko, Natalia Kopteva
A two-dimensional slice through the parameter space of two-generator Kleinian groups. Int. J. Algebra Comput. 28 (8) (2018)
Natalia Kopteva
Energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes. Numerische Mathematik 137 (3) (2017)
Natalia Kopteva, Martin Stynes
Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem. Adv. Comput. Math. 43 (1) (2017)
Natalia Kopteva, Torsten Linß
Improved maximum-norm a posteriori error estimates for linear and semilinear parabolic equations. Adv. Comput. Math. 43 (5) (2017)
Alan Demlow, Natalia Kopteva
Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems. Numerische Mathematik 133 (4) (2016)
Natalia Kopteva
Maximum-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes. SIAM J. Numer. Anal. 53 (6) (2015)
Natalia Kopteva
Linear finite elements may be only first-order pointwise accurate on anisotropic triangulations. Math. Comput. 83 (289) (2014)
Natalia Kopteva, Torsten Linß
Maximum Norm A Posteriori Error Estimation for Parabolic Problems Using Elliptic Reconstructions. SIAM J. Numer. Anal. 51 (3) (2013)
Natalia Kopteva, Torsten Linß
Maximum Norm a Posteriori Error Estimation For a Time-dependent Reaction-diffusion Problem. Comput. Methods Appl. Math. 12 (2) (2012)
Natalia Kopteva, Torsten Linß
Numerical Study of Maximum Norm a Posteriori Error Estimates for Singularly Perturbed Parabolic Problems. NAA (2012)
Natalia Kopteva, Maria Pickett
A second-order overlapping Schwarz method for a 2D singularly perturbed semilinear reaction-diffusion problem. Math. Comput. 81 (277) (2012)
Natalia Kopteva, Martin Stynes
Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem. Numerische Mathematik 119 (4) (2011)
Naresh M. Chadha, Natalia Kopteva
Maximum norm a posteriori error estimate for a 3d singularly perturbed semilinear reaction-diffusion problem. Adv. Comput. Math. 35 (1) (2011)
Vladimir B. Andreev, Natalia Kopteva
-shaped domain. Math. Comput. 77 (264) (2008)
Natalia Kopteva
Maximum Norm A Posteriori Error Estimate for a 2D Singularly Perturbed Semilinear Reaction-Diffusion Problem. SIAM J. Numer. Anal. 46 (3) (2008)
Natalia Kopteva
Numerical Analysis of a 2d Singularly Perturbed Semilinear Reaction-Diffusion Problem. NAA (2008)
Andrew C. Fowler, Natalia Kopteva, Charles Oakley
The Formation of River Channels. SIAM J. Appl. Math. 67 (4) (2007)
Natalia Kopteva
Maximum norm error analysis of a 2d singularly perturbed semilinear reaction-diffusion problem. Math. Comput. 76 (258) (2007)
Martin Stynes, Natalia Kopteva
Numerical analysis of singularly perturbed nonlinear reaction-diffusion problems with multiple solutions. Comput. Math. Appl. 51 (5) (2006)
Natalia Kopteva, Niall Madden, Martin Stynes
Grid equidistribution for reaction-diffusion problems in one dimension. Numer. Algorithms 40 (3) (2005)
Elena Klimenko, Natalia Kopteva
Groups Whose Generators have Real Traces. Int. J. Algebra Comput. 15 (3) (2005)
Natalia Kopteva
Error Expansion for an Upwind Scheme Applied to a Two-Dimensional Convection-Diffusion Problem. SIAM J. Numer. Anal. 41 (5) (2003)
Natalia Kopteva
Maximum Norm A Posteriori Error Estimates for a One-Dimensional Convection-Diffusion Problem. SIAM J. Numer. Anal. 39 (2) (2001)
Natalia Kopteva, Martin Stynes
A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem. SIAM J. Numer. Anal. 39 (4) (2001)
Natalia Kopteva
Uniform Pointwise Convergence of Difference Schemes for Convection-Diffusion Problems on Layer-Adapted Meshes. Computing 66 (2) (2001)