The Finite Element Method for Parabolic Equations. I. A Posteriori Error Estimation
The Finite Element Method for Parabolic Equations. II. A Posteriori Error Estimation and Adaptive Approach
The local solution of a parabolic-elliptic equation with a nonlinear Neumann boundary condition
We investigate a parabolic-elliptic problem, where the time derivative is multiplied by a coefficient which may vanish on time-dependent spatial subdomains. The linear equation is supplemented by a nonlinear Neumann boundary condition with a locally defined, -bounded function . We prove the existence of a local weak solution to the problem by means of the Rothe method. A uniform a priori estimate for the Rothe approximations in , which is required by the local assumptions on , is derived by...
The Method of Lines for Poisson's Equation with Nonlinear or Free Boundary Conditions.
The Numerical Solution Of Elliptic Partial Differential Equations By The Method Of Lines.
The Rothe method and time periodic solutions to the Navier-Stokes equations and equations of magnetohydrodynamics
The existence of a periodic solution of a nonlinear equation is proved. The theory developed may be used to prove the existence of a periodic solution of the variational formulation of the Navier-Stokes equations or the equations of magnetohydrodynamics. The proof of the main existence theorem is based on Rothe method in combination with the Galerkin method, using the Brouwer fixed point theorem.
Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method
We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG) methods. The output of this detector is a reliably scaled, element-wise smoothness estimate which is suited as a control input to a shock capture mechanism. Using an artificial viscosity in the latter role, we obtain a DG scheme for the numerical solution of nonlinear systems of conservation laws. Building on work by Persson and Peraire, we thoroughly justify the...
Метод прямых в применении к некоторым двумерным нелинейным параболическим уравнениям
О применении многоточечной дифференциально-разностной схемы к одной краевой задаче
Оценки решений двухточечных задач для систем обыкновенных дифференциальных уравнений первого порядка и метод прямых
Равномерная сходимость метода прямых в случае первой краевой задачи для нелинейного параболического уравнения второго порядка
Равномерная сходимость неявной схемы метода сеток решения первой краевой задачи для нелинейного параболического уравнения второго порядка
Сходимость метода прямых в случае первой периодически-краевой задачи нелинейного параболического уравнения второго порядка
Сходимость с порядком (2p+1)-точечной схемы метода прямых для одной краевой задачи