From 12f6e93111b8f434e33c3e741d7dae72563a28e0 Mon Sep 17 00:00:00 2001
From: Christoph Lehmann <christoph.lehmann@ufz.de>
Date: Fri, 2 Sep 2016 14:49:11 +0200
Subject: [PATCH] [Doc] added formulae

---
 .../process/convergence_criterion/DeltaX/c_DeltaX.md          | 4 +++-
 .../PerComponentDeltaX/c_PerComponentDeltaX.md                | 4 +++-
 .../PerComponentResidual/c_PerComponentResidual.md            | 4 +++-
 .../process/convergence_criterion/Residual/c_Residual.md      | 4 +++-
 4 files changed, 12 insertions(+), 4 deletions(-)

diff --git a/Documentation/ProjectFile/process/convergence_criterion/DeltaX/c_DeltaX.md b/Documentation/ProjectFile/process/convergence_criterion/DeltaX/c_DeltaX.md
index c235efb07af..b65a0efd3d1 100644
--- a/Documentation/ProjectFile/process/convergence_criterion/DeltaX/c_DeltaX.md
+++ b/Documentation/ProjectFile/process/convergence_criterion/DeltaX/c_DeltaX.md
@@ -6,4 +6,6 @@ the norm of the whole solution vector, i.e., the entirety of all process
 variables.
 
 At least one of the relative or absolute tolerance has to be met in order to
-satisfy this convergence criterion.
+satisfy this convergence criterion, i.e., the following has to hold (with errors
+\f$e\f$ and tolerances \f$t\f$):
+\f[ e_{\mathrm{abs}} \le t_{\mathrm{abs}} \vee e_{\mathrm{rel}} \le t_{\mathrm{rel}} \f]
diff --git a/Documentation/ProjectFile/process/convergence_criterion/PerComponentDeltaX/c_PerComponentDeltaX.md b/Documentation/ProjectFile/process/convergence_criterion/PerComponentDeltaX/c_PerComponentDeltaX.md
index 8fbeb585ce0..ebec3bba907 100644
--- a/Documentation/ProjectFile/process/convergence_criterion/PerComponentDeltaX/c_PerComponentDeltaX.md
+++ b/Documentation/ProjectFile/process/convergence_criterion/PerComponentDeltaX/c_PerComponentDeltaX.md
@@ -7,4 +7,6 @@ vectorial process variable, to each vector component) of the solution vector
 individually.
 
 For each component at least one of the relative or absolute tolerance has to be
-met in order to satisfy this convergence criterion.
+met in order to satisfy this convergence criterion, i.e., the following has to
+hold (with errors \f$e\f$ and tolerances \f$t\f$):
+\f[ e_{\mathrm{abs}} \le t_{\mathrm{abs}} \vee e_{\mathrm{rel}} \le t_{\mathrm{rel}} \f]
diff --git a/Documentation/ProjectFile/process/convergence_criterion/PerComponentResidual/c_PerComponentResidual.md b/Documentation/ProjectFile/process/convergence_criterion/PerComponentResidual/c_PerComponentResidual.md
index 62512cfd897..7189e9cfa5e 100644
--- a/Documentation/ProjectFile/process/convergence_criterion/PerComponentResidual/c_PerComponentResidual.md
+++ b/Documentation/ProjectFile/process/convergence_criterion/PerComponentResidual/c_PerComponentResidual.md
@@ -7,4 +7,6 @@ vectorial process variable, to each vector component) of the residuum vector
 individually.
 
 For each component at least one of the relative or absolute tolerance has to be
-met in order to satisfy this convergence criterion.
+met in order to satisfy this convergence criterion, i.e., the following has to
+hold (with errors \f$e\f$ and tolerances \f$t\f$):
+\f[ e_{\mathrm{abs}} \le t_{\mathrm{abs}} \vee e_{\mathrm{rel}} \le t_{\mathrm{rel}} \f]
diff --git a/Documentation/ProjectFile/process/convergence_criterion/Residual/c_Residual.md b/Documentation/ProjectFile/process/convergence_criterion/Residual/c_Residual.md
index a5d4846796a..d9347b3cc52 100644
--- a/Documentation/ProjectFile/process/convergence_criterion/Residual/c_Residual.md
+++ b/Documentation/ProjectFile/process/convergence_criterion/Residual/c_Residual.md
@@ -5,4 +5,6 @@ A relative and/or absolute tolerance value can be specified, which is applied to
 the norm of the whole residuum vector.
 
 At least one of the relative or absolute tolerance has to be met in order to
-satisfy this convergence criterion.
+satisfy this convergence criterion, i.e., the following has to hold (with errors
+\f$e\f$ and tolerances \f$t\f$):
+\f[ e_{\mathrm{abs}} \le t_{\mathrm{abs}} \vee e_{\mathrm{rel}} \le t_{\mathrm{rel}} \f]
-- 
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