Implementing Galerkin Finite Element Methods for Semilinear Elliptic Differential Inclusions
-
Janosch Rieger
Abstract.
This paper presents the first feasible method for the approximation of solution sets
of semi-linear elliptic partial differential inclusions. It is based on a new Galerkin Finite Element
approach that projects the original differential inclusion to a finite-dimensional subspace of 
.
The problem that remains is to discretize the unknown solution set of the resulting finite-dimensional
algebraic inclusion in such a way that efficient algorithms for its computation can be designed
and error estimates can be proved.
One such discretization and the corresponding basic algorithm are presented along with several enhancements, and the algorithm is applied to two model problems.
© 2013 by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Masthead
- A Robust Preconditioned MinRes Solver for Time-periodic Eddy Current Problems
- Robust Approximation of Singularly Perturbed Delay Differential Equations by the hp Finite Element Method
- On Cardinal Spline Interpolation
- Convection Problems on Anisotropic Meshes
- Pointwise Error Estimates for the LDG Method Applied to 1-d Singularly Perturbed Reaction-Diffusion Problems
- Implementing Galerkin Finite Element Methods for Semilinear Elliptic Differential Inclusions
Articles in the same Issue
- Masthead
- A Robust Preconditioned MinRes Solver for Time-periodic Eddy Current Problems
- Robust Approximation of Singularly Perturbed Delay Differential Equations by the hp Finite Element Method
- On Cardinal Spline Interpolation
- Convection Problems on Anisotropic Meshes
- Pointwise Error Estimates for the LDG Method Applied to 1-d Singularly Perturbed Reaction-Diffusion Problems
- Implementing Galerkin Finite Element Methods for Semilinear Elliptic Differential Inclusions
