scholarly journals The DPG Method for the Convection-Reaction Problem Revisited.

2021 ◽  
Author(s):  
Leszek Demkowicz ◽  
Nathan Roberts
Keyword(s):  
Reaction Problem

A HIERARCHICAL A POSTERIORI ERROR ESTIMATE FOR AN ADVECTION-DIFFUSION-REACTION PROBLEM

2005 ◽  
Vol 15 (07) ◽  
pp. 1119-1139 ◽  
Author(s):  
RODOLFO ARAYA ◽  
ABNER H. POZA ◽  
ERNST P. STEPHAN
Keyword(s):  
Error Estimate ◽  
Posteriori Error ◽  
A Posteriori Error Estimate ◽  
Diffusion Reaction ◽  
Posteriori Error Estimate ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Advection Diffusion ◽  
Norm Of The Error ◽  
Reaction Problem

In this work we introduce a new a posteriori error estimate of hierarchical type for the advection-diffusion-reaction equation. We prove the equivalence between the energy norm of the error and our error estimate using an auxiliary linear problem for the residual and an easy way to prove inf–sup condition.

scholarly journals New Analytical Solutions for Time-Fractional Kolmogorov–Petrovsky–Piskunov Equation with Variety of Initial Boundary Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 813
Author(s):  
Thanon Korkiatsakul ◽  
Sanoe Koonprasert ◽  
Khomsan Neamprem
Keyword(s):  
Boundary Conditions ◽  
Analytical Solutions ◽  
Initial Boundary ◽  
Operational Matrices ◽  
Analytical Approximations ◽  
Chebyshev Wavelet ◽  
Caputo Fractional Order Derivative ◽  
Shift Chebyshev Polynomial ◽  
Generalized Time ◽  
Reaction Problem

The generalized time fractional Kolmogorov–Petrovsky–Piskunov equation (FKPP), D t α ω ( x , t ) = a ( x , t ) D x x ω ( x , t ) + F ( ω ( x , t ) ) , which plays an important role in engineering, chemical reaction problem is proposed by Caputo fractional order derivative sense. In this paper, we develop a framework wavelet, including shift Chebyshev polynomial of the first kind as a mother wavelet, and also construct some operational matrices that represent Caputo fractional derivative to obtain analytical solutions for FKPP equation with three different types of Initial Boundary conditions (Dirichlet, Dirichlet–Neumann, and Neumann–Robin). Our results shown that the Chebyshev wavelet is a powerful method, due to its simplicity, efficiency in analytical approximations, and its fast convergence. The comparison of the Chebyshev wavelet results indicates that the proposed method not only gives satisfactory results but also do not need large amount of CPU times.

COMBINING ADJOINT STABILIZED METHODS FOR THE ADVECTION-DIFFUSION-REACTION PROBLEM

2007 ◽  
Vol 17 (02) ◽  
pp. 305-326 ◽  
Author(s):  
GUILLERMO HAUKE ◽  
GIANCARLO SANGALLI ◽  
MOHAMED H. DOWEIDAR
Keyword(s):  
Piecewise Linear ◽  
Diffusion Reaction ◽  
One Dimensional ◽  
Stabilized Methods ◽  
Advection Diffusion ◽  
Diffusive Limit ◽  
Reaction Transport ◽  
Globally Stable ◽  
Supg Method ◽  
Reaction Problem

Computational methods for the advection-diffusion-reaction transport equation are still a challenge. Although there exist globally stable methods, oscillations around sharp layers such as boundary, inner and outflow layers, are typical in multi-dimensional flows. In this paper a variational formulation that combines two types of stabilization integrals is proposed, namely an adjoint stabilization and a gradient adjoint stabilization. Two free parameters are chosen by imposing one-dimensional superconvergence. Then, when applied to multi-dimensional flows, the method presents better local stability than the present stabilized methods. Furthermore, in the advective-diffusive limit and for piecewise linear functional spaces, the method recovers the classical SUPG method.

Problems In Realistic Modelling Of Interfacial Reactions

1985 ◽  
Vol 54 ◽  
Author(s):  
Charles W. Allen ◽  
Gordon A Sargent
Keyword(s):  
Single Phase ◽  
Driving Forces ◽  
Thermodynamic Description ◽  
Nucleation Theory ◽  
Initial Reaction ◽  
Thermodynamic Prediction ◽  
Multiple Product ◽  
Solid Liquid ◽  
Reaction Processes ◽  
Reaction Problem

ABSTRACTFor modelling the reaction of chemically distinct materials in which intermediate alloy phases are formed a simple thermodynamic description is not adequate. Despite thermodynamic prediction of multiple product phases, a single phase generally forms first which is not necessarily that of greatest thermodynamic stability or of simplest structure. Such initial reaction processes may be modelled as metastable perltectoid (solid-solid) or perltectlc (solid-liquid) reactions, characterized by large thermodynamic driving forces with superimposed kinetic and morphological constraints. The interfacial reaction problem is reviewed in light of heterogeneous nucleation theory with emphasis on non-classical aspects.

scholarly journals Interpretations and Naturalness in the Radiation-Reaction Problem

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 658
Author(s):  
Carlos Barceló ◽  
Luis Garay ◽  
Jaime Redondo-Yuste
Keyword(s):  
Internal Structure ◽  
Equivalence Principle ◽  
Large Body ◽  
Radiation Reaction ◽  
Classical Electrodynamics ◽  
New Research ◽  
Reaction Problem ◽  
Radiation Reaction Problem

After more than a century of history, the radiation-reaction problem in classical electrodynamics still surprises and puzzles new generations of researchers. Here, we revise and explain some of the paradoxical issues that one faces when approaching the problem, mostly associated with regimes of uniform proper acceleration. The answers we provide can be found in the literature and are a synthesis of a large body of research. We only present them in a personal way that may help in their understanding. Besides, after the presentation of the standard answers, we motivate and present a twist to those ideas. The physics of emission of radiation by extended charges (charges with internal structure) might proceed in a surprising oscillating fashion. This hypothetical process could open up new research paths and a new take on the equivalence principle.

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