In this work, we introduce a new space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable, and a modified Hilbert transformation is used. For this resulting variational setting, ansatz and test spaces are equal. Thus, conforming finite element discretizations lead to Galerkin--Bubnov schemes. We consider a conforming tensor-product approach with piecewise polynomial, continuous basis functions, which results in an unconditionally stable method, i.e., no CFL condition is required. We give numerical examples for a one- and a two-dimensional spatial domain, where the unconditional stability and optimal convergence rates in space-time norms are illustrated.
翻译：在这项工作中,我们引入了二阶波方程的新的时空变换配方,即对时间变量也采用各部分的集成,并使用经修改的Hilbert转换。对于由此产生的变异环境,安萨兹和试验空间是相等的。因此,符合有限元素分解导致加勒金-布布诺夫计划。我们考虑采用符合单向多元基连续功能的抗压产品法,从而产生一种无条件稳定的方法,即不需要CFL条件。我们给出一个一维和二维空间域的数字示例,说明空间时间规范的无条件稳定性和最佳趋同率。
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