scholarly journals A strategy to implement Dirichlet boundary conditions in the context of ADER finite volume schemes. One-dimensional conservation laws

2016 ◽  
Vol 140 ◽  
pp. 357-370
Author(s):  
Gino I. Montecinos
Keyword(s):  
Boundary Conditions ◽  
Conservation Laws ◽  
Finite Volume ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Finite Volume Schemes ◽  
One Dimensional

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

scholarly journals Triple solutions for a Dirichlet boundary value problem involving a perturbed discrete p(k)-Laplacian operator

2017 ◽  
Vol 15 (1) ◽  
pp. 1075-1089 ◽  
Author(s):  
Mohsen Khaleghi Moghadam ◽  
Johnny Henderson
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Local Minimum ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Laplacian Operator ◽  
Discrete Problem ◽  
Dirichlet Boundary Value Problem ◽  
One Dimensional ◽  
Minimum Theorem

Abstract Triple solutions are obtained for a discrete problem involving a nonlinearly perturbed one-dimensional p(k)-Laplacian operator and satisfying Dirichlet boundary conditions. The methods for existence rely on a Ricceri-local minimum theorem for differentiable functionals. Several examples are included to illustrate the main results.

Mild singular potentials as effective Laplacians in narrow strips

2017 ◽  
Vol 120 (1) ◽  
pp. 145
Author(s):  
César R. De Oliveira ◽  
Alessandra A. Verri
Keyword(s):  
Boundary Conditions ◽  
Quadratic Forms ◽  
Dirichlet Boundary ◽  
Schrödinger Operators ◽  
Dirichlet Boundary Conditions ◽  
Schrodinger Operators ◽  
Singular Potentials ◽  
One Dimensional ◽  
Effective Operators

We propose to obtain information on one-dimensional Schrödinger operators on bounded intervals by approaching them as effective operators of the Laplacian in thin planar strips.  Here we develop this idea to get spectral knowledge of some mild singular potentials with Dirichlet boundary conditions.  Special preparations, including a result on perturbations of quadratic forms, are included as well.

scholarly journals Further results for a one-dimensional linear thermoelastic equation with Dirichlet-Dirichlet boundary conditions

2002 ◽  
Vol 43 (3) ◽  
pp. 449-462 ◽  
Author(s):  
Bao Zhu Guo
Keyword(s):  
Hilbert Space ◽  
Boundary Conditions ◽  
Riesz Basis ◽  
Dirichlet Boundary ◽  
The State ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Parallel Result ◽  
Generalized Eigenfunctions ◽  
Thermoelastic Equation

AbstractWe show that a sequence of generalized eigenfunctions of a one-dimensional linear thermoelastic system with Dirichiet-Dirichlet boundary conditions forms a Riesz basis for the state Hilbert space. This develops a parallel result for the same system with Dirichlet-Neumann or Neumann-Dirichlet boundary conditions.

scholarly journals A SIMPLE ALGORITHM TO ENFORCE DIRICHLET BOUNDARY CONDITIONS IN COMPLEX GEOMETRIES

2011 ◽  
Vol 22 (10) ◽  
pp. 1093-1105 ◽  
Author(s):  
CHRISTIAN HUBER ◽  
JOSEF DUFEK ◽  
BASTIEN CHOPARD
Keyword(s):  
Phase Transition ◽  
Boundary Conditions ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Dirichlet Boundary ◽  
Simple Algorithm ◽  
Dirichlet Boundary Conditions ◽  
Pure Substance ◽  
Complex Geometries ◽  
High Symmetry

We present a new algorithm to implement Dirichlet boundary conditions for diffusive processes in arbitrarily complex geometries. In this approach, the boundary conditions around the diffusing object is replaced by the fictitious phase transition of a pure substance where the energy cost of the phase transition largely overwhelms the amount of energy stored in the system. The computing cost of this treatment of the boundary condition is independent of the topology of the boundary. Moreover, the implementation of this new approach is straightforward and follows naturally from enthalpy-based numerical methods. This algorithm is compatible with a wide variety of discretization methods, finite differences, finite volume, lattice Boltzmann methods and finite elements, to cite a few. We show, here, using both lattice Boltzmann and finite-volume methods that our model is in excellent agreement with analytical solutions for high symmetry geometries. We also illustrate the advantages of the algorithm to handle more complex geometries.

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