Nonlinear Sobolev Equations Research Articles

Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions

We derive optimal L 2 error estimates for semi-discrete finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions. A new projection is introduced and used in the error analysis.

Galerkin methods for nonlinear Sobolev equations

We study Galerkin approximations to the solution of nonlinear Sobolev equations with homogeneous Dirichlet boundary condition in two spatial dimensions and derive optimalL2 error estimates for the continuous Crank — Nicolson and Extrapolated Crank — Nicolson approximations.

Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension

A semidiscrete Galerkin finite element method is defined and analyzed for nonlinear evolution equations of Sobolev type in a single space variable. Optimal orderL p error estimates are derived for 2?p??. And it is shown that the rates of convergence of the approximate solution and its derivative are one order better than the optimal order at certain spatial Jacobi and Gauss points, respectively. Also the standard nodal superconvergence results are established. Futher, it is considered that an a posteriori procedure provides superconvergent approximations at the knots for the spatial derivatives of the exact solution.