### Department of Mathematics and Systems Analysis

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Here are the reports authored by Sergey Korotov. See the reports of all authors.

- A570
**Discrete maximum principles for FEM solutions of nonlinear elliptic systems**[pdf][ps]- Received 2009-05-20 * elliptic system, finite element method, discrete maximum principle * AMS 65N50, 65M50 * 53 pages
- A567
**On a bisection algorithm that produces conforming locally refined simplicial meshes**[pdf][ps]- Received 2009-04-09 * bisection algorithm, simplicial elements, conforming finite element method, local refinements, nested meshes * AMS 65N50, 65M50 * 11 pages
- A563
**Goal-oriented a posteriori error estimates for transport problems**[pdf][ps]- Received 2009-02-10 * stationary convection-diffusion equations, the finite element method, a posteriori error estimates, goal-oriented quantities, mesh adaptation * AMS 65N15, 65N50, 76M30 * 16 pages
- A561
**On nodal superconvergence in 3D by averaging piecewise linear, bilinear, and trilinear FE approximations**[pdf][ps]- Received 2008-12-02 * higher order error estimates, tetrahedral and prismatic elements, superconvergence, averaging operators * AMS 65N30 * 13 pages
- A559
**On a discrete maximum principle for linear FE solutions of elliptic problems with a nondiagonal coefficient matrix**[pdf][ps]- Received 2008-11-28 * discrete maximum principle, finite element method, acute triangulations, full diffusion tensor * AMS 65N30, 65N50 * 10 pages
- A552
**A discrete maximum principle in Hilbert space with applications to nonlinear cooperative elliptic systems**[pdf][ps]- Received 2008-08-26 * elliptic system, maximum principles, finite element method, discrete maximum principle * AMS 65N30, 65N50 * 40 pages
- A551
**Discrete maximum principles for the FEM solution of some nonlinear parabolic problems**[pdf][ps]- Received 2008-08-26 * nonlinear parabolic problems, discrete maximum principle, finite element method * AMS 65M60, 65M50, 35B50 * 24 pages
- A550
**Discrete maximum principles for FE solutions of nonstationary diffusion-reaction problems with mixed boundary conditions**[pdf][ps]- Received 2008-08-26 * nonstationary diffusion-reaction problem, maximum principle, mixed boundary conditions, linear finite elements, discrete maximum principle, simplicial partition, angle condition * AMS 65M60, 65M50, 35B50 * 21 pages
- A549
**On weakening conditions for discrete maximum principles for linear finite element schemes**[pdf][ps]- Received 2008-08-26 * elliptic equations, maximum principles, finite element method, discrete maximum principle, monotone matrix, matrix irreducibility * AMS 65N30, 65N50 * 9 pages
- A527
**Sharp upper global a posteriori error estimates for nonlinear elliptic variational problems**[pdf][ps] abstract: [pdf][ps]- Received 2007-08-08 * a posteriori error estimation, error control in energy norm, error estimates of functional type, elliptic equation of second order, elliptic equation of fourth order, second order elasticity system, mixed boundary conditions * AMS 65J05, 65J15, 65M60, 65N15, 65N30, 65N50 * 47 pages
- A525
**The discrete maximum principle for linear simplicial finite element approximations of a reaction-diffusion problem**[pdf][ps] abstract: [pdf][ps]- Received 2007-07-13 / Revised 2007-07-18 * reaction-diffusion problem, maximum principle, finite element method, discrete maximum principle, simplicial partition, angle condition * AMS 65N30, 65N50 * 16 pages
- A524
**A new a posteriori error estimate for convection-reaction-diffusion problems**[pdf][ps] abstract: [pdf][ps]- Received 2007-05-23 * convection-reaction-diffusion, a posteriori error estimation, adaptivity * AMS 65N15, 65N50, 76M30 * 12 pages
- A522
**A posteriori error estimates for some problems in linear elasticity**[pdf][ps] abstract: [pdf][ps]- Received 2007-03-27 * a posteriori error estimation, local errors, superconvergence, finite element method, linear elasticity, fracture mechanics * AMS 65N15, 65N30, 65N50 * 14 pages
- A521
**Strong regularity of a family of face-to-face partitions generated by the longest-edge bisection algorithm**[pdf][ps] abstract: [pdf][ps]- Received 2007-04-24 * Zlamal's minimum angle condition, simplicial elements, conforming finite element method, nested partitions * AMS 65M50, 65N30 * 18 pages
- A517
**Simplicial finite elements in higher dimensions**[pdf][ps] abstract: [pdf][ps]- Received 2007-02-07 * n-simplex, finite element method, superconvergence, strengthened Cauchy-Schwarz inequality, discrete maximum principle * AMS 65N30, 51M20 * 16 pages
- A515
**Global a posteriori error estimates for convection-reaction-diffusion problems**[pdf][ps] abstract: [pdf][ps]- Received 2006-12-08 * convection-reaction-diffusion equation, a posteriori error estimation, Friedrichs-Poincare inequality * AMS 65N15, 65N50, 76M30 * 13 pages
- A510
**Discrete maximum principles for FEM solutions of some nonlinear elliptic interface problems**[pdf][ps] abstract: [pdf][ps]- Received 2006-12-07 * nonlinear elliptic problem, interface problem, maximum principle, discrete maximum principle, finite element method, simplicial mesh * AMS 35B50, 35J65, 65N30, 65N50 * 23 pages
- A506
**Error control in terms of linear functionals based on gradient averaging techniques**[pdf][ps] abstract: [pdf][ps]- Received 2006-07-26 * a posteriori error estimation, quantity of interest, finite element method, differential equation of elliptic type, linear elasticity, superconvergence * AMS 65N15, 65N30, 65N50 * 13 pages
- A505
**On the equivalence of regularity criteria for triangular and tetrahedral finite element partitions**[pdf][ps] abstract: [pdf][ps]- Received 2006-07-26 * finite element method, inscribed ball, circumscribed ball, regular family of simplicial partitions, Zl'amal's condition * AMS 65N12, 65N30 * 11 pages
- A504
**On discrete maximum principles for nonlinear elliptic problems**[pdf][ps] abstract: [pdf][ps]- Received 2006-07-26 * nonlinear elliptic problem, mixed boundary conditions, discrete maximum principle, finite element method, quadratures * AMS 65N30, 65N50, 35B50, 35J65 * 17 pages
- A503
**On acute and nonobtuse simplicial partitions**[pdf][ps] abstract: [pdf][ps]- Received 2006-07-25 * ortho-simplices, path-simplices, Delaunay triangulation, Kuhn partition, polytope * AMS 51M20, 65N30 * 17 pages
- A498
**Goal-oriented error estimates based on different FE-spaces for the primal and the dual problem with applications to fracture mechanics**[pdf][ps] abstract: [pdf][ps]- Received 2006-03-16 * A posteriori error estimation, finite elements, fracture mechanics * AMS 65N15, 65N30, 65N50, 74R10 * 24 pages
- A496
**Dissection of the path-simplex in R^n into n path-subsimplices**[pdf][ps] abstract: [pdf][ps]- Received 2006-03-03 * n-simplex, path-simplex, Coxeter's trisection, self-similarity * AMS 51M20, 65N30 * 15 pages
- A495
**A posteriori error estimation for linear elliptic problems with mixed boundary conditions**[pdf][ps] abstract: [pdf][ps]- Received 2006-03-03 * reliable computations, a posteriori error estimation, error control in energy norm, differential equation of elliptic type, mixed boundary conditions * AMS 65N15, 65N30 * 14 pages
- A494
**Computational technologies for reliable control of global and local errors for linear elliptic type boundary value problems**[pdf][ps] abstract: [pdf][ps]- Received 2006-02-16 * a posteriori error estimation, error control in energy norm, error control in terms of linear functionals, differential equation of elliptic type, mixed boundary conditions, gradient averaging * AMS 65N15, 65N30 * 23 pages

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