Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains.
Numerische Quadratur bei Projektionsverfahren.
O jednoznačnosti a nejednoznačnosti řešení rovnic
O triangulacích bez tupých úhlů
Object oriented design philosophy for scientific computing
This contribution gives an overview of current research in applying object oriented programming to scientific computing at the computational mechanics laboratory (LABMEC) at the school of civil engineering – UNICAMP. The main goal of applying object oriented programming to scientific computing is to implement increasingly complex algorithms in a structured manner and to hide the complexity behind a simple user interface. The following areas are current topics of research and documented within the...
Object oriented design philosophy for scientific computing
This contribution gives an overview of current research in applying object oriented programming to scientific computing at the computational mechanics laboratory (LABMEC) at the school of civil engineering – UNICAMP. The main goal of applying object oriented programming to scientific computing is to implement increasingly complex algorithms in a structured manner and to hide the complexity behind a simple user interface. The following areas are current topics of research and documented within the...
Observations Regarding Algorithms Required for Robust CFD Codes
Over the last three decades Computational Fluid Dynamics (CFD) has gradually joined the wind tunnel and flight test as a primary flow analysis tool for aerodynamic designers. CFD has had its most favorable impact on the aerodynamic design of the high-speed cruise configuration of a transport. This success has raised expectations among aerodynamicists that the applicability of CFD can be extended to the full flight envelope. However, the complex nature...
On a 2D vector Poisson problem with apparently mutually exclusive scalar boundary conditions
On a 2D vector Poisson problem with apparently mutually exclusive scalar boundary conditions
This work is devoted to the study of a two-dimensional vector Poisson equation with the normal component of the unknown and the value of the divergence of the unknown prescribed simultaneously on the entire boundary. These two scalar boundary conditions appear prima facie alternative in a standard variational framework. An original variational formulation of this boundary value problem is proposed here. Furthermore, an uncoupled solution algorithm is introduced together with its finite element...
On a certain two-sided symmetric condition in magnetic field analysis and computations
A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity...
On a conjugate semi-variational method for parabolic equations
On a conjugate semi-variational method for parabolic equations
On a conservation upwind finite element scheme for convective diffusion equations
On a construction of fast direct solvers
Fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra are constructed. The domain given is extended by symmetrization or skew symmetrization onto a rectangle or a rectangular parallelepiped and a fast direct solver is used there. All extendable domains are found. Eigenproblems are also considered.
On a hierarchical basis multilevel method with nonconforming P1 elements.
On a method of two-sided eigenvalue estimates for elliptic equations of the form
The Collatz method of twosided eigenvalue estimates was extended by K. Rektorys in his monography Variational Methods to the case of differential equations of the form with elliptic operators. This method requires to solve, successively, certain boundary value problems. In the case of partial differential equations, these problems are to be solved approximately, as a rule, and this is the source of further errors. In the work, it is shown how to estimate these additional errors, or how to avoid...
On a Mixed Finite Element Approximation of the Stokes Problem (I). Convergence of the Approximate Solutions.
On a mixed finite element method for the Stokes problem in
On a multilevel Krylov method for the Helmholtz equation preconditioned by shifted Laplacian.
On a noncoercive system of quasi-variational inequalities related to stochastic control problems.