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The maximum principle is a basic qualitative property of the solution of second-order elliptic boundary value problems. The preservation of the qualitative characteristics, such as the maximum principle, in discrete model is one of the key requirements. It is well known that standard linear finite element solution does not satisfy maximum principle on… (More)

- Richard Liska, Burton Wendroff
- SIAM J. Scientific Computing
- 2003

- Richard Liska, Stanly L. Steinberg
- Comput. J.
- 1993

- Hoon Hong, Richard Liska, Stanly L. Steinberg
- J. Symb. Comput.
- 1997

- Richard Liska, Mikhail Yu. Shashkov, Victor G. Ganzha
- Mathematics and Computers in Simulation
- 2004

The support operator method designs mimetic finite difference schemes by first constructing a discrete divergence operator based on the divergence theorem, and then defining the discrete gradient operator as the adjoint operator of the divergence based on the Gauss theorem connecting the divergence and gradient operators, which remains valid also in the… (More)

- Richard Liska, L. Drsda
- ISSAC
- 1990

The article deals with automation of the process of numerical solving of partial differential equations systems (PDES) by means of computer algebra. For solving PDES the finite difference method is applied. The computer algebra system REDUCE and the numerical programming language FORTRAN are used in the methodology presented, its main aim being to speed up… (More)

A finite difference algorithm for solution of generalized Laplace equation on unstructured triangular grid is constructed by a support operator method. The support operator method first constructs discrete divergence operator from the divergence theorem and then constructs discrete gradient operator as the adjoint operator of the divergence. The adjointness… (More)

- Richard Liska, Mikhail Yu. Shashkov, Pavel Váchal, Burton Wendroff
- J. Comput. Physics
- 2010

A new optimization-based synchronized flux-corrected conservative interpolation (remap-ping) of mass and momentum for arbitrary Lagrangian–Eulerian hydro methods is described. Fluxes of conserved variables – mass and momentum – are limited in a synchronous way to preserve local bounds of primitive variables – density and velocity. In numerical simulations… (More)

- C Abdallah, P Dorato, R Liska, S Steinberg, W Yang
- 1995

The maximum principle is basic qualitative property of the solution of elliptic boundary value problems. The preservation of the qualitative characteristics, such as maximum principle, in discrete model is one of the key requirements. It is well known that standard linear finite element solution does not satisfy maximum principle on general triangular… (More)