The block-grid method for solving Laplace's equation on polygons with nonanalytic boundary conditions.
The frequency decomposition multi-grid method. II. Convergence analysis based on the additive Schwarz method.
The L.P.D.E.M., a mixed finite difference method for elliptic problems.
The mixed problem for the Laplace equation on the rectangle
The Numerical Computation of Compressed States of Nonlinearly Elastic Anisotropic Plates.
The Numerical Solution of a Model Problem Biharmonic Equation by Using Extrapolated Altering Direction Implicit Methods.
The Numerical Solution of a Periodic Parabolic Problem Subject to a Nonlinear Boundary Condition. II.
The point source function of the mixed difference problem in the half-plane
The Robbins problem for elliptic equations in space
Thermal ablation modeling via the bioheat equation and its numerical treatment
The phenomenon of thermal ablation is described by Pennes' bioheat equation. This model is based on Newton's law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.
Transfer of boundary conditions for difference equations
It is well-known that the idea of transferring boundary conditions offers a universal and, in addition, elementary means how to investigate almost all methods for solving boundary value problems for ordinary differential equations. The aim of this paper is to show that the same approach works also for discrete problems, i.e., for difference equations. Moreover, it will be found out that some results of this kind may be obtained also for some particular two-dimensional problems.
Transformation of Three-Dimensional Regions onto Rectangular Regions by Elliptic Systems.
Two free-boundary problems with singularities
Two Numerical Methods for the elliptic Monge-Ampère equation
The numerical solution of the elliptic Monge-Ampère Partial Differential Equation has been a subject of increasing interest recently [Glowinski, in 6th International Congress on Industrial and Applied Mathematics, ICIAM 07, Invited Lectures (2009) 155–192; Oliker and Prussner, Numer. Math.54 (1988) 271–293; Oberman, Discrete Contin. Dyn. Syst. Ser. B10 (2008) 221–238; Dean and Glowinski, in Partial differential equations, Comput. Methods Appl. Sci. 16 (2008) 43–63; Glowinski et al., Japan...
Two-level nonlinear elimination based preconditioners for inexact Newton methods with application in shocked duct flow calculation.
Uniform convergence of monotone iterative methods for semilinear singularly perturbed problems of elliptic and parabolic types.
Uniformly Convergent Difference Schemes for Singularly Perturbed Parabolic Diffusion-Convection Problems Without Turning Points.
Vorzeichenstabile Differenzenverfahren für parabolische Anfangsrandwertaufgaben.
Wave-ray multigrid method for standing wave equations.
Weighted Sobolev descent for singular first order partial differential equations.