The numerical solution of PDE problems with standard software packages

Design Principles of Reusable Software Components for the Numerical Solution of Pde Problems 1.2 Component Libraries

We rst present some general considerations about software for Scientiic Computing and argue in favor of a component-oriented approach. Algorithmic components are identiied as rewarding but also demanding targets for reuse by means of generic programming. In the second part we examine in more detail the interaction of algorithms and grid data structures, and show how numerical procedures can be ...

Fourth-order numerical solution of a fractional PDE with the nonlinear source term in the electroanalytical chemistry

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...

On the convergence of right transforming iterations for the numerical solution of PDE-constrained optimization problems

Numerical Techniques for Optimization Problems with PDE Constraints

Optimization problems with partial differential equation (PDE) constraints arise in many science and engineering applications. Their robust and efficient solution present many mathematical challenges and requires a tight integration of properties and structures of the underlying problem, of fast numerical PDE solvers, and of numerical nonlinear optimization. This workshop brought together exper...

Interplay between discretization and algebraic compu- tation in adaptive numerical solution of elliptic PDE problems

The Adaptive Finite Element Method (AFEM) for approximating solutions of PDE boundary value and eigenvalue problems is a numerical scheme that automatically and iteratively adapts the finite element space until a sufficiently accurate approximate solution is found. The adaptation process is based on a posteriori error estimators, and at each step of this process an algebraic problem (linear or ...