1. A class of pseudo-parabolic equations: existence, uniqueness of weak solutions, and error estimates for the Euler-implicit discretization Author Ioan Pop, Y Yabin Fan, Center for Analysis, Scientific Computing & Appl., Applied Analysis - BURGERS, and Applied Analysis Subjects Discretization, General Mathematics, Weak solution, Mathematical analysis, General Engineering, Finite difference method, Explicit and implicit methods, Exponential integrator, Euler equations, symbols.namesake, symbols, Euler's formula, Uniqueness, Mathematics Abstract In this paper, we investigate a class of pseudo-parabolic equations. Such equations model two-phase flow in porous media where dynamic effects are included in the capillary pressure. The existence and uniqueness of a weak solution are proved, and error estimates for an Euler implicit time discretization are obtained. Copyright © 2011 John Wiley & Sons, Ltd. Published 2011
2. Convergence analysis of a vertex-centered finite volume scheme for a copper heap leaching model Author Mauricio Sepúlveda, Emilio Cariaga, Ioan Pop, Fernando Concha, Center for Analysis, Scientific Computing & Appl., and Applied Analysis Subjects Finite volume method, Compact space, General Mathematics, Ordinary differential equation, Mathematical analysis, General Engineering, Neumann boundary condition, Heap leaching, Godunov's scheme, Finite volume method for one-dimensional steady state diffusion, Finite element method, Mathematics Abstract In this paper a two-dimensional solute transport model is considered to simulate the leaching of copper ore tailing using sulfuric acid as the leaching agent. The mathematical model consists in a system of differential equations: two diffusion–convection-reaction equations with Neumann boundary conditions, and one ordinary differential equation. The numerical scheme consists in a combination of finite volume and finite element methods. A Godunov scheme is used for the convection term and an P1-FEM for the diffusion term. The convergence analysis is based on standard compactness results in L2. Some numerical examples illustrate the effectiveness of the scheme. Copyright © 2009 John Wiley & Sons, Ltd. Published 2010
3. Exact constants in Poincaré type inequalities for functions with zero mean boundary traces Author Sergey Repin and Alexander I. Nazarov Subjects Zero mean, Partial differential equation, eigenvalue problems, General Mathematics, Mathematical analysis, ta111, General Engineering, Boundary (topology), Value (computer science), Type (model theory), Physics::History of Physics, Poincare type inequalities, symbols.namesake, Lipschitz domain, error estimates, Poincaré conjecture, symbols, functional inequalities, Mathematics Abstract In this paper, we investigate Poincare type inequalities for the functions having zero mean value on the whole boundary of a Lipschitz domain or on a measurable part of the boundary. We find exact and easily computable constants in these inequalities for some basic domains (rectangles, cubes, and right triangles) and discuss applications of the inequalities to quantitative analysis of partial differential equations. Copyright © 2014 John Wiley & Sons, Ltd. Published 2015