Coupled Finite Element Analysis for Semi-implicit Linear and Fully-implicit Nonlinear Scheme in Partially Saturated Porous Medium

Analysis of an Euler Implicit - Mixed Finite Element Scheme for Reactive Solute Transport in Porous Media

Abstract. In this paper we analyze an Euler implicit-mixed finite element scheme for a porous media solute transport model. The transporting flux is not assumed given, but obtained by solving numerically the Richards equation, a model for sub-surface fluid flow. We prove the convergence of the scheme by estimating the error in terms of the discretization parameters. In doing so we take into acc...

Error Analysis of Linearized Semi-implicit Galerkin Finite Element Methods for Nonlinear Parabolic Equations

This paper is concerned with the time-step condition of commonly-used linearized semi-implicit schemes for nonlinear parabolic PDEs with Galerkin finite element approximations. In particular, we study the time-dependent nonlinear Joule heating equations. We present optimal error estimates of the semi-implicit Euler scheme in both the L norm and the H norm without any time-step restriction. Theo...

Asynchronous Evolution for Fully-Implicit and Semi-Implicit Time Integration

We propose a series of techniques for hybridizing implicit and semi-implicit time integration methods in a manner that retains much of the speed of the implicit method without sacrificing all of the higher quality vibrations one obtains with methods that handle elastic forces explicitly. We propose our scheme in the context of asynchronous methods, where different parts of the mesh are evolved ...

Semi-implicit Scheme for the Spectral Element Atmospheric Model

A Linearly Implicit Finite-Difference Scheme for the One-Dimensional Porous Medium Equation

We present and analyze a linearly implicit finite-difference scheme for computing approximate solutions and interface curves for the porous medium equation in one space variable. Our scheme requires only that linear, tridiagonal systems of equations be solved at each time step. We derive error bounds for the approximate interface curves as well as for the approximate solutions under the rather ...