Finite element approaches generally do not guarantee exact satisfaction of conservation laws especially when Dirichlet-type boundary conditions are imposed. This article discusses improvement of the global mass conservation property of quasi-bubble nite element solutions for the shallow water equations, focusing on implementations of the surface-elevation boundary conditions. We propose two alt...

The existence of equilibrium solutions to reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales is proved by the topological degree theory and M-matrix method. Under some sufficient conditions, we obtain the uniqueness and global exponential stability of equilibrium solution to reaction-diffusion recurrent neural networks with Dirichlet boundary conditio...

An immersed-boundary method, previously developed for flow-field simulation, is extended to study heat-transfer problems of flow over a circular cylinder. The Dirichlet-type isothermal temperature boundary conditions and the Neumann-type iso-heat-flux boundary conditions are both implemented. To verify the accuracy of the simulation method, L2-norm are computed to test the order of accuracy of ...

Boundary value problems for second-order elliptic equations in divergence form, whose nonlinearity is governed by a convex function of non-necessarily power type, are considered. The global boundedness their solutions established under boundary conditions Dirichlet, or Neumann, Robin type. A decisive role the results played optimal forms Orlicz-Sobolev embeddings and trace embeddings, which all...

A finite element numerical method is investigated for fractional order elliptic boundary value problems with homogeneous Dirichlet type boundary conditions. It is pointed out that an appropriate stiffness matrix can be obtained by taking the prescribed fractional power of the stiffness matrix corresponding to the non-fractional elliptic operators. It is proved that this approach, which is also ...

In this paper we provide‎ ‎existence results for positive solution to‎ ‎Dirichlet p(t)-Laplacian boundary value problems‎. ‎The sublinear and‎ ‎superlinear cases are considerd‎.

The paper presents the semi-numerical solution for the magnetohydrodynamic (MHD) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. The governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (NODE) by using a classical similarity transformation along with appropriate boundary cond...

Let M be a compact Riemannian manifold with smooth boundary. We obtain the exact long time asymptotic behaviour of the heat kernel on abelian coverings ofM with mixed Dirichlet and Neumann boundary conditions. As an application, we study the long time behaviour of the abelianized winding of reflected Brownian motions in M . In particular, we prove a Gaussian type central limit theorem showing t...

We propose a hybrid Smoothed Particle Hydrodynamics solver for efficiently simulating incompressible fluids using an interface handling method for boundary conditions in the pressure Poisson equation. We blend particle density computed with one smooth and one spiky kernel to improve the robustness against both fluid-fluid and fluid-solid collisions. To further improve the robustness and efficie...