Mixed finite element methods for elliptic problems
Computer Methods in Applied Mechanics and Engineering
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Analysis and implementation of TR-BDF2
Applied Numerical Mathematics
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Wave Propagation in Infinite Domains: With Applications to Structure Interaction
Wave Propagation in Infinite Domains: With Applications to Structure Interaction
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From a macroscopic perspective, saturated porous materials like soils represent volumetrically interacting solid---fluid aggregates. They can be properly modelled using continuum porous media theories accounting for both solid-matrix deformation and pore-fluid flow. The dynamic excitation of such multi-phase materials gives rise to different types of travelling waves, where it is of common interest to adequately describe their propagation through unbounded domains. This poses challenges for the numerical treatment and demands special solution strategies that avoid artificial and numerically-induced perturbations or interferences. The present paper is concerned with the accurate and stable numerical solution of dynamic wave propagation problems in infinite half spaces. Proceeding from an isothermal, biphasic, linear poroelasticity model with incompressible constituents, finite elements are used to discretise the near field and infinite elements to approximate the far field. The transient propagation of the poroacoustic body waves to the infinity is thereby modelled by a viscous damping boundary, which, for stability reasons, necessitates an appropriate treatment of the included velocity-dependent damping forces.