Finite element approximation of a sixth order nonlinear degenerate parabolic equation
نویسندگان
چکیده
منابع مشابه
Finite element approximation of a sixth order nonlinear degenerate parabolic equation
We consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation ut = ∇.( b(u)∇∆u), where generically b(u) := |u| for any given γ ∈ (0,∞). In addition to showing well-posedness of our approximation, we prove convergence in space dimensions d ≤ 3. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. Finally some num...
متن کاملFinite element approximation of a fourth order nonlinear degenerate parabolic equation
We consider a fully practical nite element approximation of the fourth order nonlinear degenerate parabolic equation u t + r:(b(u)ru)= 0; where generically b(u) := juj p for any given p 2 (0; 1). An iterative scheme for solving the resulting nonlinear discrete system is analysed. In addition to showing well-posedness of our approximation, we prove convergence in one space dimension. Finally som...
متن کاملA Sixth-Order Nonlinear Parabolic Equation for Quantum Systems
The global-in-time existence of weak nonnegative solutions to a sixth-order nonlinear parabolic equation in one space dimension with periodic boundary conditions is proved. The equation arises from an approximation of the quantum drift-diffusion model for semiconductors and describes the evolution of the electron density in the semiconductor crystal. The existence result is based on two techniq...
متن کاملFinite Element Approximation for Degenerate Parabolic Equations. an Application of Nonlinear Semigroup Theory
Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and L contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in L and L∞, respectively, of the scheme are e...
متن کاملOptimal order finite element approximation for a hyperbolic integro-differential equation
Semidiscrete finite element approximation of a hyperbolic type integro-differential equation is studied. The model problem is treated as the wave equation which is perturbed with a memory term. Stability estimates are obtained for a slightly more general problem. These, based on energy method, are used to prove optimal order a priori error estimates.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 2004
ISSN: 0029-599X,0945-3245
DOI: 10.1007/s00211-003-0479-4