High-order finite element methods for the Kuramoto-Sivashinsky equation
Finite element discretization of the Kuramoto-Sivashinsky equation
We analyze semidiscrete and second-order in time fully discrete finite element methods for the Kuramoto-Sivashinsky equation.
Galerkin time-stepping methods for nonlinear parabolic equations
We consider discontinuous as well as continuous Galerkin methods for the time discretization of a class of nonlinear parabolic equations. We show existence and local uniqueness and derive optimal order optimal regularity a priori error estimates. We establish the results in an abstract Hilbert space setting and apply them to a quasilinear parabolic equation.
Galerkin time-stepping methods for nonlinear parabolic equations
We consider discontinuous as well as continuous Galerkin methods for the time discretization of a class of nonlinear parabolic equations. We show existence and local uniqueness and derive optimal order optimal regularity error estimates. We establish the results in an abstract Hilbert space setting and apply them to a quasilinear parabolic equation.
Finite difference discretization of the Kuramoto-Sivashinsky equation.
Solving the systems of equations arising in the discretization of some nonlinear p.d.e.'s by implicit Runge-Kutta methods
Finite difference discretization with variable mesh of the Schrodinger equation in a variable domain
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