47 citations · 87 across the 16 of their papers we have counts for
23 papers
Space-time finite element methods for nonlinear wave equations via elliptic regularisation
Lehel Banjai, Emmanuil H. Georgoulis, Brian Hennessy
We present and analyse a new conforming space-time Galerkin discretisation of a semi-linear wave equation, based on a variational formulation derived from De Giorgi's elliptic regu…
Generalized convolution quadrature based on the trapezoidal rule
Lehel Banjai, Matteo Ferrari
We present a novel generalized convolution quadrature method that accurately approximates convolution integrals. During the late 1980s, Lubich introduced convolution quadrature tec…
Runge-Kutta convolution quadrature based on Gauss methods
Lehel Banjai, Matteo Ferrari
An error analysis of Runge-Kutta convolution quadrature based on Gauss methods applied to hyperbolic operators is given. The order of convergence relies heavily on the parity of th…
Numerical analysis of a time-stepping method for the Westervelt equation with time-fractional damping
Katherine Baker, Lehel Banjai, Mariya Ptashnyk
We develop a numerical method for the Westervelt equation, an important equation in nonlinear acoustics, in the form where the attenuation is represented by a class of non-local in…
A modified convolution quadrature combined with the method of fundamental solutions and Galerkin BEM for acoustic scattering
Ebraheem Aldahham, Lehel Banjai
We describe a numerical method for the solution of acoustic exterior scattering problems based on the time-domain boundary integral representation of the solution. As the spatial d…
Implicit/explicit, BEM/FEM coupled scheme for acoustic waves with the wave equation in the second order formulation
Lehel Banjai
Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and…
A posteriori error analysis for approximations of time-fractional subdiffusion problems
Lehel Banjai, Charalambos G. Makridakis
In this paper we consider a sub-diffusion problem where the fractional time derivative is approximated either by the L1 scheme or by Convolution Quadrature. We propose new interpre…
Numerical analysis of a wave equation for lossy media obeying a frequency power law
Katherine Baker, Lehel Banjai
We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we pr…
Exponential Convergence of FEM for Spectral Fractional Diffusion in Polygons
Lehel Banjai, Jens M. Melenk, Christoph Schwab
For the spectral fractional diffusion operator of order in bounded, curvilinear polygonal domains we prove exponential convergence of two classes of discreti…
Strong convergence of a Verlet integrator for the semi-linear stochastic wave equation
Lehel Banjai, Gabriel Lord, Jeta Molla
The full discretization of the semi-linear stochastic wave equation is considered. The discontinuous Galerkin finite element method is used in space and analyzed in a semigroup fra…
Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature
Lehel Banjai, Christian Lubich, Joerg Nick
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the materia…
-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains
Lehel Banjai, Jens M. Melenk, Christoph Schwab
In bounded, polygonal domains with Lipschitz boundary consisting of a finite number of Jordan curves admitting analytic parametrizations, we ana…
Numerical approximation of the Schrödinger equation with concentrated potential
Lehel Banjai, María López-Fernández
We present a family of algorithms for the numerical approximation of the Schrödinger equation with potential concentrated at a finite set of points. Our methods belong to the so-ca…
A PDE approach to fractional diffusion: a space-fractional wave equation
Lehel Banjai, Enrique Otarola
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order , of symmetric, coercive,…
Efficient high order algorithms for fractional integrals and fractional differential equations
Lehel Banjai, María López-Fernández
We propose an efficient algorithm for the approximation of fractional integrals by using Runge--Kutta based convolution quadrature. The algorithm is based on a novel integral repre…
Computation of sharp estimates of the Poincaré constant on planar domains with piecewise self-similar boundary
Lehel Banjai, Lyonell Boulton
We establish a strategy for finding sharp upper and lower numerical bounds of the Poincaré constant on a class of planar domains with piecewise self-similar boundary. The approach…
Tensor FEM for spectral fractional diffusion
Lehel Banjai, Jens M. Melenk, Ricardo H. Nochetto +3
We design and analyze several Finite Element Methods (FEMs) applied to the Caffarelli-Silvestre extension that localizes the fractional powers of symmetric, coercive, linear ellipt…
Runge--Kutta convolution coercivity and its use for time-dependent boundary integral equations
Lehel Banjai, Christian Lubich
A coercivity property of temporal convolution operators is an essential tool in the analysis of time-dependent boundary integral equations and their space and time discretisations.…
A Trefftz polynomial space-time discontinuous Galerkin method for the second order wave equation
Lehel Banjai, Emmanuil H. Georgoulis, Oluwaseun Lijoka
A new space-time discontinuous Galerkin (dG) method utilising special Trefftz polynomial basis functions is proposed and fully analysed for the scalar wave equation in a second ord…
Fast and oblivious algorithms for dissipative and 2D wave equations
Lehel Banjai, María López-Fernández, Achim Schädle
The use of time-domain boundary integral equations has proved very effective and efficient for three dimensional acoustic and electromagnetic wave equations. In even dimensions and…
Convolution quadrature for the wave equation with a nonlinear impedance boundary condition
Lehel Banjai, Alexander Rieder
A rarely exploited advantage of time-domain boundary integral equations compared to their frequency counterparts is that they can be used to treat certain nonlinear problems. In th…
Stable numerical coupling of exterior and interior problems for the wave equation
Lehel Banjai, Christian Lubich, Francisco-Javier Sayas
Stable numerical coupling of exterior and interior problems for the wave equation
Fully discrete Kirchhoff formulas with CQ-BEM
Lehel Banjai, Antonio Laliena, Francisco-Javier Sayas
In this paper we propose and analyze a fully discrete method for a direct boundary integral formulation of the scattering of a transient acoustic wave by a sound-soft obstacle. The…